Commit 2024-01-07 11:52 de9d093d
View on Github →feat: add trans assoc type lemmas for (Partial)Equiv and (Partial)Homeomorph (#9506)
Let es denote Equivs and fs denote PartialEquivs. 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
eandfflipped - (2) with
eandfflipped The definitionsEquiv.transPartialEquivandPartialEquiv.transEquivare 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.transandPartialEquiv.trans. The same is done forHomeomorph/PartialHomeomorph.