Commit 2024-01-07 11:52 de9d093d
View on Github →feat: add trans assoc type lemmas for (Partial)Equiv
and (Partial)Homeomorph
(#9506)
Let e
s denote Equiv
s and f
s denote PartialEquiv
s. Let >
denote Equiv.trans
, PartialEquiv.trans
, Equiv.transPartialEquiv
, or PartialEquiv.transEquiv
. We want to simplify expressions like e1 > e2 > f3 > f4 > e5 > e6
to (e1 > e2) > (f3 > f4) > (e5 > e6)
, so that simp lemmas about Equiv.trans
and PartialEquiv.trans
may apply. This means adding four lemmas:
e1 > e2 > f3 = (e1 > e2) > f3
(e1 > f2) > f3 = e1 > (f2 > f3)
- (1) with
e
andf
flipped - (2) with
e
andf
flipped The definitionsEquiv.transPartialEquiv
andPartialEquiv.transEquiv
are moved to later in the document, so that they stay together with these lemmas. The argument order of these two definitions has also been reversed so as to matchEquiv.trans
andPartialEquiv.trans
. The same is done forHomeomorph
/PartialHomeomorph
.