English
If two subgroups s and t of G are equal, then the quotients G/s and G/t are canonically bijective.
Русский
Если две подгруппы s и t равны, то соответственно квадраты G/s и G/t гранично биективны.
LaTeX
$$$\alpha \cong \beta$ whenever $s = t$ with the quotient construction$$
Lean4
/-- If two subgroups `M` and `N` of `G` are equal, their quotients are in bijection. -/
@[to_additive /-- If two subgroups `M` and `N` of `G` are equal, their quotients are in bijection. -/
]
def quotientEquivOfEq (h : s = t) : α ⧸ s ≃ α ⧸ t
where
toFun := Quotient.map' id fun _a _b h' => h ▸ h'
invFun := Quotient.map' id fun _a _b h' => h.symm ▸ h'
left_inv q := induction_on q fun _g => rfl
right_inv q := induction_on q fun _g => rfl
