diff options
Diffstat (limited to 'mathcomp')
| -rw-r--r-- | mathcomp/ssreflect/eqtype.v | 14 |
1 files changed, 10 insertions, 4 deletions
diff --git a/mathcomp/ssreflect/eqtype.v b/mathcomp/ssreflect/eqtype.v index 1391b5b..1225ad9 100644 --- a/mathcomp/ssreflect/eqtype.v +++ b/mathcomp/ssreflect/eqtype.v @@ -220,10 +220,13 @@ Lemma contraFeq b x y : (x != y -> b) -> b = false -> x = y. Proof. by move=> imp /negbT; apply: contraNeq. Qed. Lemma contraPeq P x y : (x != y -> ~ P) -> P -> x = y. -Proof. by move => imp HP; apply: contraTeq isT => /imp /(_ HP). Qed. +Proof. by move=> imp HP; apply: contraTeq isT => /imp /(_ HP). Qed. Lemma contra_not_eq P x y : (x != y -> P) -> ~ P -> x = y. -Proof. by move => imp; apply: contraPeq => /imp HP /(_ HP). Qed. +Proof. by move=> imp; apply: contraPeq => /imp HP /(_ HP). Qed. + +Lemma contra_not_neq P x y : (x = y -> P) -> ~ P -> x != y. +Proof. by move=> imp; apply: contra_notN => /eqP. Qed. Lemma contraTneq b x y : (x = y -> ~~ b) -> b -> x != y. Proof. by move=> imp; apply: contraTN => /eqP. Qed. @@ -235,7 +238,7 @@ Lemma contraFneq b x y : (x = y -> b) -> b = false -> x != y. Proof. by move=> imp /negbT; apply: contraNneq. Qed. Lemma contraPneq P x y : (x = y -> ~ P) -> P -> x != y. -Proof. by move => imp; apply: contraPN => /eqP. Qed. +Proof. by move=> imp; apply: contraPN => /eqP. Qed. Lemma contra_eqN b x y : (b -> x != y) -> x = y -> ~~ b. Proof. by move=> imp /eqP; apply: contraL. Qed. @@ -255,8 +258,11 @@ Proof. by move=> imp; apply: contraNF => /imp->. Qed. Lemma contra_neqT b x y : (~~ b -> x = y) -> x != y -> b. Proof. by move=> imp; apply: contraNT => /imp->. Qed. +Lemma contra_eq_not P x y : (P -> x != y) -> x = y -> ~ P. +Proof. by move=> imp /eqP; apply: contraTnot. Qed. + Lemma contra_neq_not P x y : (P -> x = y) -> x != y -> ~ P. -Proof. by move => imp;apply: contraNnot => /imp->. Qed. +Proof. by move=> imp;apply: contraNnot => /imp->. Qed. Lemma contra_eq z1 z2 x1 x2 : (x1 != x2 -> z1 != z2) -> z1 = z2 -> x1 = x2. Proof. by move=> imp /eqP; apply: contraTeq. Qed. |