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src/finlattice.v

Lines changed: 7 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -426,6 +426,8 @@ Record finLattice :=
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premeet_closed L^~pl elements &
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elements != fset0]}.
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(*TODO: separate the conjunction into three separate fields*)
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Canonical finLattice_subType := Eval hnf in [subType for elements].
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Definition finLattice_eqMixin := Eval hnf in [eqMixin of finLattice by <:].
@@ -678,6 +680,7 @@ Definition fin_joinMixin := JoinRelMixin finjoinC finjoinA lefinjoin.
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Local Canonical fin_meetOrder := MeetOrder finle finlt finmeet fin_meetMixin.
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Local Canonical fin_joinOrder := JoinOrder finle finlt finjoin fin_joinMixin.
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Local Canonical fin_lattice := [lattice of finle].
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(* TODO : are these canonical declarations mandatory ?*)
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End FinLatticeStructure.
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Module Exports.
@@ -1363,6 +1366,7 @@ Local Canonical tbJoinOrder := [tbJoinOrder of finle].
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Local Canonical bLattice := [bLattice of finle].
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Local Canonical tLattice := [tLattice of finle].
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Local Canonical tbLattice := [tbLattice of finle].
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(* TODO : are canonical declarations mandatory ?*)
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End FinTBLatticeStructure.
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Module Exports.
@@ -1488,7 +1492,8 @@ Lemma coatomP {L} {S : {finLattice L}} {a} : reflect
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([/\ a \in S, (a <_L \ftop_S) &
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forall x, x \in S -> x <_L \ftop_S -> ~~(a <_L x)])
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(coatom S a).
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Proof. apply/(iffP idP).
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Proof.
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apply/(iffP idP).
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- by move/atomP.
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- move=> ?; exact/atomP.
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Qed.
@@ -1783,7 +1788,7 @@ Qed.
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Lemma dual_itv_r L (S : {finLattice L}) a b :
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([<a; b>]_S)^~s = [< b ; a>]_(S^~s).
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Proof. by apply/val_inj/Interval.dual_itv_fset_eq. Qed.
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Proof. by apply/val_inj/Interval.dual_itv_fset_eq. Qed.
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Definition dual_itv :=
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(@dual_itv_r, fun L => @dual_itv_r [preLattice of dual_rel <=:L]).

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