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Merged
CohenCyril merged 3 commits into from
Jan 19, 2021
Merged

iff lemmas #320

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8e3d704
iff lemmas
affeldt-aist Jan 14, 2021
c64655e
Update theories/boolp.v
affeldt-aist Jan 19, 2021
b924734
fix and changelog update
affeldt-aist Jan 19, 2021
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1 change: 1 addition & 0 deletions CHANGELOG_UNRELEASED.md
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Expand Up @@ -17,6 +17,7 @@
- in `classical_sets.v`, lemmas `subset_has_lbound`, `subset_has_ubound`

- in `reals.v`, lemmas `sup_setU`, `inf_setU`
- in `boolp.v`, lemmas `iff_notr`, `iff_not2`

### Changed

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6 changes: 6 additions & 0 deletions theories/boolp.v
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Expand Up @@ -366,6 +366,12 @@ Lemma notLR P Q : (P = ~ Q) -> (~ P) = Q. Proof. exact: canLR notK. Qed.

Lemma notRL P Q : (~ P) = Q -> P = ~ Q. Proof. exact: canRL notK. Qed.

Lemma iff_notr (P Q : Prop) : (P <-> ~ Q) <-> (~ P <-> Q).
Proof. by split=> [/propext ->|/propext <-]; rewrite notK. Qed.

Lemma iff_not2 (P Q : Prop) : (~ P <-> ~ Q) <-> (P <-> Q).
Proof. by split=> [/iff_notr|PQ]; [|apply/iff_notr]; rewrite notK. Qed.

(* -------------------------------------------------------------------- *)
(* assia : let's see if we need the simplpred machinery. In any case, we sould
first try definitions + appropriate Arguments setting to see whether these
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