LeftCosetEquivalence — Mathlib

English

Two left cosets a•s and b•s are equal exactly when a•s = b•s.

Русский

Две левые косеты a•s и b•s равны тогда и только тогда, когда a•s = b•s.

LaTeX

$$LeftCosetEquivalence(s,a,b) := (a\,\,\,s = b\,\,\,s)$$

Lean4

/-- Equality of two left cosets `a * s` and `b * s`. -/
@[to_additive LeftAddCosetEquivalence /-- Equality of two left cosets `a + s` and `b + s`. -/
    ]
def LeftCosetEquivalence (s : Set α) (a b : α) :=
  a • s = b • s

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