Commit 2023-04-03 20:45 e655e4ea
View on Github →feat(algebra/group_power/lemmas): Induction principle for powers (#18668)
A property holds for all powers of g
if it is holds for 1
and is preserved under multiplication and division by g
.
Also rename subgroup.zpowers_subset
/add_subgroup.zmultiples_subset
to subgroup.zpowers_le_of_mem
/add_subgroup.zmultiples_le_of_mem
because there is no ⊆
in the statement.
The motivation is the Cauchy-Davenport theorem:
https://github.com/leanprover-community/mathlib/blob/321b67021163ac504c6cfa35d5678a47b357869d/src/combinatorics/additive/cauchy_davenport.lean#L176-L181