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| author | Cyril Cohen | 2017-11-16 14:28:06 +0100 |
|---|---|---|
| committer | Cyril Cohen | 2017-11-23 20:27:58 +0100 |
| commit | ea271b82db4a090ea4d3939baba814d2d077513d (patch) | |
| tree | 2e80d7b0965d165317e95656451dd1a9659bd740 | |
| parent | 82739c704bef2234dce643cbdd0b5be5a79b755b (diff) | |
Add addrKA and subrKA (addrK and addrNK modulo Associativity)
| -rw-r--r-- | mathcomp/algebra/ssralg.v | 6 |
1 files changed, 6 insertions, 0 deletions
diff --git a/mathcomp/algebra/ssralg.v b/mathcomp/algebra/ssralg.v index 9d93608..8ae63b8 100644 --- a/mathcomp/algebra/ssralg.v +++ b/mathcomp/algebra/ssralg.v @@ -732,6 +732,12 @@ Proof. by apply: (canRL (addrK x)); rewrite addrC subKr. Qed. Lemma opprD : {morph -%R: x y / x + y : V}. Proof. by move=> x y; rewrite -[y in LHS]opprK opprB addrC. Qed. +Lemma addrKA z x y : (x + z) - (z + y) = x - y. +Proof. by rewrite opprD addrA addrK. Qed. + +Lemma subrKA z x y : (x - z) + (z - y) = x - y. +Proof. by rewrite addrA addrNK. Qed. + Lemma subr0_eq x y : x - y = 0 -> x = y. Proof. by rewrite -(subrr y) => /addIr. Qed. |