Eqv — Mathlib

Lean4
/-- The relation on `FreeAddMonoid (M × N)` that generates a congruence whose quotient is
the tensor product. -/
inductive Eqv : FreeAddMonoid (M × N) → FreeAddMonoid (M × N) → Prop
  | of_zero_left : ∀ n : N, Eqv (.of (0, n)) 0
  | of_zero_right : ∀ m : M, Eqv (.of (m, 0)) 0
  | of_add_left : ∀ (m₁ m₂ : M) (n : N), Eqv (.of (m₁, n) + .of (m₂, n)) (.of (m₁ + m₂, n))
  | of_add_right : ∀ (m : M) (n₁ n₂ : N), Eqv (.of (m, n₁) + .of (m, n₂)) (.of (m, n₁ + n₂))
  | of_smul : ∀ (r : R) (m : M) (n : N), Eqv (.of (r • m, n)) (.of (m, r • n))
  | add_comm : ∀ x y, Eqv (x + y) (y + x)
Похожие утверждения