refactor(library/standard/set): use the same style for mem_inter and mem_union

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2014-07-27 13:32:59 -07:00
parent 88130f339e
commit 99a1966fd6

View file

@ -32,9 +32,7 @@ theorem mem_inter (x : T) (A B : set T) : x ∈ A ∩ B ↔ (x ∈ A ∧ x ∈ B
(assume H,
have e1 : A x = '1, from and_elim_left H,
have e2 : B x = '1, from and_elim_right H,
calc A x && B x = '1 && B x : {e1}
... = '1 && '1 : {e2}
... = '1 : band_b1_left '1)
show A x && B x = '1, from e1⁻¹ ▸ e2⁻¹ ▸ band_b1_left '1)
theorem inter_comm (A B : set T) : A ∩ B = B ∩ A
:= funext (λx, band_comm (A x) (B x))