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fact
string | imports
string | filename
string | symbolic_name
string | __index_level_0__
int64 |
|---|---|---|---|---|
Variable not_D : int -> int -> int -> bool.
|
mathcomp(all_ssreflect all_algebra) shift bigopz
|
coq-community-apery/punk
|
coq-community-apery
| 729 |
Definition z3 : creal rat := CReal creal_z3seq.
|
mathcomp(all_ssreflect all_algebra) mathcomp(bigenough cauchyreals) extra_mathcomp extra_cauchyreals tactics shift bigopz arithmetics seq_defs c_props s_props z3seq_props a_props b_props b_over_a_props
|
coq-community-apery/z3irrational
|
coq-community-apery
| 730 |
Definition b_over_a := CReal creal_b_over_a_seq.
|
mathcomp(all_ssreflect all_algebra) mathcomp(bigenough cauchyreals) extra_mathcomp extra_cauchyreals tactics shift bigopz arithmetics seq_defs c_props s_props z3seq_props a_props b_props b_over_a_props
|
coq-community-apery/z3irrational
|
coq-community-apery
| 731 |
Definition Kdelta := ubound (6%:Q%:CR * z3)%CR.
|
mathcomp(all_ssreflect all_algebra) mathcomp(bigenough cauchyreals) extra_mathcomp extra_cauchyreals tactics shift bigopz arithmetics seq_defs c_props s_props z3seq_props a_props b_props b_over_a_props
|
coq-community-apery/z3irrational
|
coq-community-apery
| 732 |
Definition Ndelta := projT1 delta_asympt.
|
mathcomp(all_ssreflect all_algebra) mathcomp(bigenough cauchyreals) extra_mathcomp extra_cauchyreals tactics shift bigopz arithmetics seq_defs c_props s_props z3seq_props a_props b_props b_over_a_props
|
coq-community-apery/z3irrational
|
coq-community-apery
| 733 |
Definition sigma (n : nat) := (2%:Q%:CR * ((l n)%:Q ^ 3)%:CR * ((a n)%:CR * z3 - (b n)%:CR))%CR.
|
mathcomp(all_ssreflect all_algebra) mathcomp(bigenough cauchyreals) extra_mathcomp extra_cauchyreals tactics shift bigopz arithmetics seq_defs c_props s_props z3seq_props a_props b_props b_over_a_props
|
coq-community-apery/z3irrational
|
coq-community-apery
| 734 |
Definition precond_Sn (n k : int) := (n >= 0) /\ (k >= 0) /\ (n + 1 != 0) /\ (k != n + 1).
|
coq-community-apery/ops_for_nm_u
|
coq-community-apery
| 735 |
|
Definition precond_Sk (n k : int) := (n >= 0) /\ (k >= 0) /\ (n != 3%:R * k + 1) /\ (n != 3%:R * k + 2) /\ (n != 3%:R * k + 3).
|
coq-community-apery/ops_for_nm_u
|
coq-community-apery
| 736 |
|
Record Ann u : Type := ann { Sn_ : Sn u; Sk_ : Sk u }.
|
coq-community-apery/ops_for_nm_u
|
coq-community-apery
| 737 |
|
Variable ann : Ann u.
|
coq-community-apery/ops_for_nm_u
|
coq-community-apery
| 739 |
|
Definition not_D (n k : int) := (0 <= n) && (0 <= k) && (n != 3%:R * k + 1) && (n != 3%:R * k + 2) && (n != 3%:R * k + 3) && (k != n) && (k != n + 1) && (k != n + 2).
|
coq-community-apery/ops_for_nm_u
|
coq-community-apery
| 740 |
|
Definition is_fdiff_of (b a : int -> rat) := forall n : int, n >= 0 -> a (n + 1) - a n = b n.
|
BinInt mathcomp(all_ssreflect all_algebra) tactics rat_of_Z
|
coq-community-apery/rat_pos
|
coq-community-apery
| 741 |
Definition p4 (n_ : int) : rat := let n : rat := n_%:Q in rat_of_Z 12 * n^4 + rat_of_Z 96 * n^3 + rat_of_Z 283 * n^2 + rat_of_Z 364 * n + rat_of_Z 173.
|
BinInt mathcomp(all_ssreflect all_algebra) tactics rat_of_Z
|
coq-community-apery/rat_pos
|
coq-community-apery
| 742 |
Definition p3 (n_ : int) : rat := let n : rat := n_%:Q in rat_of_Z 48 * n^3 + rat_of_Z 360 * n^2 + rat_of_Z 902 * n + rat_of_Z 755.
|
BinInt mathcomp(all_ssreflect all_algebra) tactics rat_of_Z
|
coq-community-apery/rat_pos
|
coq-community-apery
| 743 |
Definition p2 (n_ : int) : rat := let n : rat := n_%:Q in rat_of_Z 144 * n^2 + rat_of_Z 864 * n + rat_of_Z 1310.
|
BinInt mathcomp(all_ssreflect all_algebra) tactics rat_of_Z
|
coq-community-apery/rat_pos
|
coq-community-apery
| 744 |
Definition p1 (n_ : int) : rat := let n : rat := n_%:Q in rat_of_Z 288 * n + rat_of_Z 1008.
|
BinInt mathcomp(all_ssreflect all_algebra) tactics rat_of_Z
|
coq-community-apery/rat_pos
|
coq-community-apery
| 745 |
Definition p0 (n_ : int) : rat := let n : rat := n_%:Q in rat_of_Z 288.
|
BinInt mathcomp(all_ssreflect all_algebra) tactics rat_of_Z
|
coq-community-apery/rat_pos
|
coq-community-apery
| 746 |
Definition Sn (n k : int) := (k != n + 1) /\ (n != -1).
|
coq-community-apery/annotated_recs_c
|
coq-community-apery
| 747 |
|
Definition Sk (n k : int) := (k + 1 != 0) /\ (n != 0).
|
coq-community-apery/annotated_recs_c
|
coq-community-apery
| 748 |
|
Definition not_D (n k : int) := (n >= 0) && (k >= 0) && (k < n).
|
coq-community-apery/annotated_recs_c
|
coq-community-apery
| 749 |
|
Definition CT (c : int -> int -> rat) := forall (n_ k_ : int), not_D n_ k_ -> P_horner (c ^~ k_) n_ = Q_flat c n_ (int.shift 1 k_) - Q_flat c n_ k_.
|
coq-community-apery/annotated_recs_c
|
coq-community-apery
| 750 |
|
Record Ann c : Type := ann { Sn_ : Sn c; Sk_ : Sk c }.
|
coq-community-apery/annotated_recs_c
|
coq-community-apery
| 751 |
|
Definition Sn2 (n k : int) := (0 <= k) /\ (k < n).
|
coq-community-apery/annotated_recs_s
|
coq-community-apery
| 752 |
|
Definition SnSk (n k : int) := (0 <= k) /\ (k < n).
|
coq-community-apery/annotated_recs_s
|
coq-community-apery
| 753 |
|
Definition Sk2 (n k : int) := (0 <= k) /\ (k + 1 < n).
|
coq-community-apery/annotated_recs_s
|
coq-community-apery
| 754 |
|
Record Ann s : Type := ann { Sn2_ : Sn2 s; SnSk_ : SnSk s; Sk2_ : Sk2 s }.
|
coq-community-apery/annotated_recs_s
|
coq-community-apery
| 755 |
|
Definition not_D (n k : int) := (k + 1 < n) && (k > 0) && (n >= 0).
|
coq-community-apery/annotated_recs_v
|
coq-community-apery
| 759 |
|
Definition CT (v : int -> int -> rat) : Prop := forall (n_ k_ : int), not_D n_ k_ -> P_horner (v ^~ k_) n_ = Q_flat v n_ (int.shift 1 k_) - Q_flat v n_ k_.
|
coq-community-apery/annotated_recs_v
|
coq-community-apery
| 760 |
|
Record Ann v : Type := ann { Sn2_ : Sn2 v; SnSk_ : SnSk v; Sk2_ : Sk2 v }.
|
coq-community-apery/annotated_recs_v
|
coq-community-apery
| 761 |
|
Fixpoint binomial_rec (n m : nat) (pn pm : bool) : int := match m, pm with | 0%N, true => 1 | _, false => 0 | m'.+1, true => let fix auxm n0 pn0 := match n0, pn0 with | 0%N, true => 0 | n0'.+1, true => binomial_rec n0' m' pn0 pm + auxm n0' pn0 | n0'.+1, false => auxm n0' pn0 - binomial_rec n0 m' pn0 pm | 0%N, false => - binomial_rec n0 m' pn0 pm end in auxm n pn end.
|
mathcomp(all_ssreflect all_algebra) tactics
|
coq-community-apery/binomialz
|
coq-community-apery
| 762 |
Definition binomialz (n m : int) : int := match n,m with | Posz n1, Posz m1 => binomial_rec n1 m1 true true | Negz n1, Posz m1 => binomial_rec n1 m1 false true | Posz n1, Negz m1 => binomial_rec n1 m1 true false | Negz n1, Negz m1 => binomial_rec n1 m1 false false end.
|
mathcomp(all_ssreflect all_algebra) tactics
|
coq-community-apery/binomialz
|
coq-community-apery
| 763 |
Fixpoint ffact_rec (n : int) (m : nat) := if m is m'.+1 then n * ffact_rec (n - 1) m' else 1.
|
mathcomp(all_ssreflect all_algebra) tactics
|
coq-community-apery/binomialz
|
coq-community-apery
| 764 |
Definition falling_factorial := nosimpl ffact_rec.
|
mathcomp(all_ssreflect all_algebra) tactics
|
coq-community-apery/binomialz
|
coq-community-apery
| 765 |
Fixpoint a (n : nat) : nat := match n with | 0 => 2 | k.+1 => (a k * (a k).-1).+1 end.
|
mathcomp(all_ssreflect all_algebra) extra_mathcomp tactics floor arithmetics multinomial
|
coq-community-apery/hanson_elem_arith
|
coq-community-apery
| 766 |
Definition a_rat (n : nat) : rat := (a n)%:Q.
|
mathcomp(all_ssreflect all_algebra) extra_mathcomp tactics floor arithmetics multinomial
|
coq-community-apery/hanson_elem_arith
|
coq-community-apery
| 767 |
Fixpoint f_k (n : nat) := match n with | 0 => 0 | n.+1 => let k0 := f_k n in if n.+1 < a k0.+1 then k0 else k0.+1 end.
|
mathcomp(all_ssreflect all_algebra) extra_mathcomp tactics floor arithmetics multinomial
|
coq-community-apery/hanson_elem_arith
|
coq-community-apery
| 768 |
Definition C_row n k := rcons (mkseq (fun i => n %/ (a i)) k) (n - (\sum_(0 <= i < k) n %/ a i)).
|
mathcomp(all_ssreflect all_algebra) extra_mathcomp tactics floor arithmetics multinomial
|
coq-community-apery/hanson_elem_arith
|
coq-community-apery
| 769 |
Definition C n k : nat := 'C[C_row n k] * (n - \sum_(0 <= i < k) n %/ a i)`!.
|
mathcomp(all_ssreflect all_algebra) extra_mathcomp tactics floor arithmetics multinomial
|
coq-community-apery/hanson_elem_arith
|
coq-community-apery
| 770 |
Definition beta (p n k : nat) := logn p (C n k).
|
mathcomp(all_ssreflect all_algebra) extra_mathcomp tactics floor arithmetics multinomial
|
coq-community-apery/hanson_elem_arith
|
coq-community-apery
| 771 |
Definition rho (i : int) : rat := a (i + 1) / a i.
|
BinInt mathcomp(all_ssreflect all_algebra) mathcomp(realalg) CoqEAL(hrel param refinements) CoqEAL(pos binnat binint rational) tactics shift binomialz bigopz rat_of_Z rho_computations seq_defs c_props initial_conds algo_closures
|
coq-community-apery/a_props
|
coq-community-apery
| 772 |
Definition beta (x : rat) : rat := ((x + rat_of_Z 1) / (x + rat_of_Z 2)) ^+ 3.
|
BinInt mathcomp(all_ssreflect all_algebra) mathcomp(realalg) CoqEAL(hrel param refinements) CoqEAL(pos binnat binint rational) tactics shift binomialz bigopz rat_of_Z rho_computations seq_defs c_props initial_conds algo_closures
|
coq-community-apery/a_props
|
coq-community-apery
| 773 |
Definition alpha (x : rat) := (rat_of_Z 17 * x ^+ 2 + rat_of_Z 51 * x + rat_of_Z 39) * (rat_of_Z 2 * x + rat_of_Z 3) / (x + rat_of_Z 2) ^+ 3.
|
BinInt mathcomp(all_ssreflect all_algebra) mathcomp(realalg) CoqEAL(hrel param refinements) CoqEAL(pos binnat binint rational) tactics shift binomialz bigopz rat_of_Z rho_computations seq_defs c_props initial_conds algo_closures
|
coq-community-apery/a_props
|
coq-community-apery
| 774 |
Definition Ka := a 1 * ((\prod_(1 <= i < Posz N_rho + 1 :> int) rho i) / 33%:Q ^+ N_rho.+1).
|
BinInt mathcomp(all_ssreflect all_algebra) mathcomp(realalg) CoqEAL(hrel param refinements) CoqEAL(pos binnat binint rational) tactics shift binomialz bigopz rat_of_Z rho_computations seq_defs c_props initial_conds algo_closures
|
coq-community-apery/a_props
|
coq-community-apery
| 775 |
Definition ghn3 : int -> rat := harmonic_numbers.ghn 3.
|
mathcomp(all_ssreflect all_algebra) binomialz bigopz
|
coq-community-apery/seq_defs
|
coq-community-apery
| 776 |
Definition c (n k : int) : rat := (binomialz n k)%:Q ^ 2 * (binomialz (n + k) k)%:Q ^ 2.
|
mathcomp(all_ssreflect all_algebra) binomialz bigopz
|
coq-community-apery/seq_defs
|
coq-community-apery
| 777 |
Definition a (n : int) : rat := \sum_(0 <= k < n + 1 :> int) (c n k).
|
mathcomp(all_ssreflect all_algebra) binomialz bigopz
|
coq-community-apery/seq_defs
|
coq-community-apery
| 778 |
Definition d (n k m : int) : rat := (-1) ^ (m + 1) / (2%:Q * m%:Q ^ 3 * (binomialz n m)%:Q * (binomialz (n + m) m)%:Q).
|
mathcomp(all_ssreflect all_algebra) binomialz bigopz
|
coq-community-apery/seq_defs
|
coq-community-apery
| 779 |
Definition s (n k : int) : rat := \sum_(1 <= m < k + 1 :> int) d n k m.
|
mathcomp(all_ssreflect all_algebra) binomialz bigopz
|
coq-community-apery/seq_defs
|
coq-community-apery
| 780 |
Definition u (n k : int) : rat := ghn3 n + s n k.
|
mathcomp(all_ssreflect all_algebra) binomialz bigopz
|
coq-community-apery/seq_defs
|
coq-community-apery
| 781 |
Definition v (n k : int) : rat := c n k * u n k.
|
mathcomp(all_ssreflect all_algebra) binomialz bigopz
|
coq-community-apery/seq_defs
|
coq-community-apery
| 782 |
Definition b (n : int) : rat := \sum_(0 <= k < n + 1 :> int) v n k.
|
mathcomp(all_ssreflect all_algebra) binomialz bigopz
|
coq-community-apery/seq_defs
|
coq-community-apery
| 783 |
Definition key := X.t.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 786 |
Parameter t : forall (A : Type) (dom : Dom.t), Type.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 787 |
Parameter empty : forall {A}, t A Dom.empty.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 788 |
Parameter is_empty : forall {A} {dom}, t A dom -> bool.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 789 |
Parameter mem : forall {A} {dom}, key -> t A dom -> bool.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 790 |
Parameter find : forall {A} {dom}, key -> t A dom -> option A.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 791 |
Parameter domain : forall {A} {dom}, t A dom -> Dom.t.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 792 |
Parameter add : forall {A} {dom} (x : key) (v : A) (m : t A dom), t A (Dom.add x dom).
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 793 |
Parameter set : forall {A} {dom} (x : key) (v : A) (m : t A dom), Dom.In x dom -> t A dom.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 794 |
Parameter remove : forall {A} {dom} x (m : t A dom), t A (Dom.remove x dom).
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 795 |
Parameter singleton : forall {A} (x : key), A -> t A (Dom.singleton x).
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 796 |
Parameter constant : forall {A} dom, A -> t A dom.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 797 |
Parameter fold : forall {A B : Type}, (key -> A -> B -> B) -> forall {dom}, t A dom -> B -> B.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 798 |
Parameter map : forall A B, (A -> B) -> forall dom, t A dom -> t B dom.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 799 |
Parameter combine : forall A B C, (A -> B -> C) -> (A -> C) -> (B -> C) -> forall dom₁ dom₂, t A dom₁ -> t B dom₂ -> t C (Dom.union dom₁ dom₂).
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 800 |
Parameter cast : forall {A} {dom₁} {dom₂}, Dom.eq dom₁ dom₂ -> t A dom₁ -> t A dom₂.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 801 |
Parameter elements : forall {A} {dom}, t A dom -> list (key * A).
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 802 |
Parameter from_elements : forall {A} (l : list (key * A)), t A (List.fold_left (fun acc xv => Dom.add (fst xv) acc) l Dom.empty).
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 803 |
Parameter empty_spec : forall A x, find x (@empty A) = None.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 804 |
Parameter is_empty_spec : forall A dom (m : t A dom), is_empty m = true <-> forall x, find x m = None.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 805 |
Parameter mem_spec : forall A x dom (m : t A dom), mem x m = true <-> exists v, find x m = Some v.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 806 |
Parameter find_spec : forall A x dom (m : t A dom), (exists v, find x m = Some v) <-> Dom.In x dom.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 807 |
Parameter domain_spec : forall A dom (m : t A dom), domain m = dom.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 808 |
Parameter set_same : forall A x v dom (m : t A dom) Hin, find x (@set A dom x v m Hin) = Some v.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 809 |
Parameter set_other : forall A x y v dom (m : t A dom) Hin, ¬X.eq y x -> find y (@set A dom x v m Hin) = find y m.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 810 |
Parameter add_same : forall A x v dom (m : t A dom), find x (add x v m) = Some v.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 811 |
Parameter add_other : forall A x y v dom (m : t A dom), ¬X.eq y x -> find y (add x v m) = find y m.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 812 |
Parameter singleton_same : forall A x (v : A), find x (singleton x v) = Some v.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 813 |
Parameter singleton_other : forall A x y (v : A), ¬X.eq y x -> find y (singleton x v) = None.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 814 |
Parameter remove_same : forall A x dom (m : t A dom), find x (remove x m) = None.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 815 |
Parameter remove_other : forall A x y dom (m : t A dom), ¬X.eq y x -> find y (remove x m) = find y m.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 816 |
Parameter constant_Some : forall A dom (v : A) x u, find x (constant dom v) = Some u <-> Dom.In x dom ∧ u = v.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 817 |
Parameter constant_None : forall A dom (v : A) x, find x (constant dom v) = None <-> ¬Dom.In x dom.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 818 |
Parameter fold_spec : forall A B (f : key -> A -> B -> B) dom (m : t A dom) (i : B), fold f m i = List.fold_left (fun acc xv => f (fst xv) (snd xv) acc) (elements m) i.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 819 |
Parameter map_spec : forall A B (f : A -> B) dom (m : t A dom) x v, find x (map f m) = Some v <-> exists u, find x m = Some u ∧ f u = v.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 820 |
Parameter combine_spec : forall A B C (f : A -> B -> C) g₁ g₂ dom₁ dom₂ (m₁ : t A dom₁) (m₂ : t B dom₂) x v, find x (combine f g₁ g₂ m₁ m₂) = Some v <-> (exists v₁ v₂, find x m₁ = Some v₁ ∧ find x m₂ = Some v₂ ∧ v = f v₁ v₂) ∨ (exists v₁, find x m₁ = Some v₁ ∧ find x m₂ = None ∧ v = g₁ v₁) ∨ (exists v₂, find x m₁ = None ∧ find x m₂ = Some v₂ ∧ v = g₂ v₂).
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 821 |
Parameter cast_spec_find : forall A dom₁ dom₂ (Heq : Dom.eq dom₁ dom₂) (m : t A dom₁) x, find x (cast Heq m) = find x m.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 822 |
Parameter elements_spec : forall A dom (m : t A dom) xv, InA (X.eq * eq)%signature xv (elements m) <-> find (fst xv) m = Some (snd xv).
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 823 |
Parameter elements_Sorted : forall A dom (m : t A dom), Sorted (X.lt@@1)%signature (elements m).
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 824 |
Parameter from_elements_spec : forall A (l : list (key * A)), NoDupA (X.eq@@1)%signature l -> forall x v, find x (from_elements l) = Some v <-> InA (X.eq * eq)%signature (x, v) l.
|
Utf8 MSets Coqlib
|
coq-contribs-dep-map/DepMapInterface
|
coq-contribs-dep-map
| 825 |
Definition OK {A} dom (map : S.t A) := ∀ x, S.In x map <-> Dom.In x dom.
|
Utf8 MSets FMaps Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapImplementation
|
coq-contribs-dep-map
| 827 |
Definition t := fun A dom => { map : S.t A | OK dom map}.
|
Utf8 MSets FMaps Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapImplementation
|
coq-contribs-dep-map
| 828 |
Definition empty : forall A, t A Dom.empty := fun A => exist (OK Dom.empty) (@S.empty A) (empty_OK A).
|
Utf8 MSets FMaps Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapImplementation
|
coq-contribs-dep-map
| 829 |
Definition is_empty (A : Type) dom (m : t A dom) := Dom.equal dom Dom.empty.
|
Utf8 MSets FMaps Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapImplementation
|
coq-contribs-dep-map
| 830 |
Definition mem (A : Type) dom (x : key) (m : t A dom) := Dom.mem x dom.
|
Utf8 MSets FMaps Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapImplementation
|
coq-contribs-dep-map
| 831 |
Definition find (A : Type) dom (x : key) (m : t A dom) := S.find x (proj1_sig m).
|
Utf8 MSets FMaps Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapImplementation
|
coq-contribs-dep-map
| 832 |
Definition domain (A : Type) dom (m : t A dom) := dom.
|
Utf8 MSets FMaps Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapImplementation
|
coq-contribs-dep-map
| 833 |
Definition add {A : Type} {dom : Dom.t} (x : key) (v : A) (m : @t A dom) : @t A (Dom.add x dom) := exist (OK (Dom.add x dom)) (S.add x v (proj1_sig m)) (add_OK x v m).
|
Utf8 MSets FMaps Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapImplementation
|
coq-contribs-dep-map
| 834 |
Definition set {A : Type} {dom : Dom.t} (x : key) (v : A) (m : @t A dom) (Hin : Dom.In x dom) := exist (OK dom) (S.add x v (proj1_sig m)) (@set_OK _ _ x v m Hin).
|
Utf8 MSets FMaps Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapImplementation
|
coq-contribs-dep-map
| 835 |
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