English
The map sending a congruence to its underlying binary relation is injective: if two congruences have the same underlying relation, they are equal.
Русский
Отображение конгруэнции к её базовой бинарнойRelation инъективно: если две конгруэнции имеют одинаковые бинарные отношения, они равны.
LaTeX
$$$\\text{ext'}:\\; c = d \\Leftarrow\\; (c\\,x\\,y) = (d\\,x\\,y)$$$
Lean4
/-- The map sending a congruence relation to its underlying binary relation is injective. -/
@[to_additive /-- The map sending an additive congruence relation to its underlying binary relation
is injective. -/
]
theorem ext' {c d : Con M} (H : ⇑c = ⇑d) : c = d :=
DFunLike.coe_injective H
