michael/lean2
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

refactor(library/algebra/ring): more robust proofs

Browse source
This commit is contained in:
Leonardo de Moura 2015-06-22 15:31:03 -07:00
parent 7ffabeb245
commit 018518f0cf
1 changed files with 6 additions and 3 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

9
library/algebra/ring.lean
View file

@ -254,11 +254,14 @@ section
include s
theorem mul_self_sub_mul_self_eq : a * a - b * b = (a + b) * (a - b) :=
by rewrite [left_distrib, *right_distrib, add.assoc, -{b*a + _}add.assoc,
-*neg_mul_eq_mul_neg, {a*b}mul.comm, add.right_inv, zero_add]
begin
krewrite [left_distrib, *right_distrib, add.assoc],
rewrite [-{b*a + _}add.assoc,
-*neg_mul_eq_mul_neg, {a*b}mul.comm, add.right_inv, zero_add]
end
theorem mul_self_sub_one_eq : a * a - 1 = (a + 1) * (a - 1) :=
mul_one 1 ▸ mul_self_sub_mul_self_eq a 1
by rewrite [-mul_self_sub_mul_self_eq, mul_one]
theorem dvd_neg_iff_dvd : (a ∣ -b) ↔ (a ∣ b) :=
iff.intro