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| author | Cyril Cohen | 2017-12-11 23:45:56 +0100 |
|---|---|---|
| committer | GitHub | 2017-12-11 23:45:56 +0100 |
| commit | f0e53dc114bdbb9d4e10098f60db45fc642fe427 (patch) | |
| tree | 975b8e0d79580f963ca50b16449b48c0b745683b /mathcomp/algebra | |
| parent | 4f4e11d3866b9d23bb629c637b35415bdd769f38 (diff) | |
| parent | 848bcdb47a7e8d8da0e1cd5530a3feadcac93ede (diff) | |
Merge pull request #160 from CohenCyril/subr_trans
Add addrKA and subrKA (addrK and addrNK modulo Associativity)
Diffstat (limited to 'mathcomp/algebra')
| -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..859bb1d 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. |