mul_left — Mathlib

English

If t is nontrivial and s is nonempty, then s * t is nontrivial.

Русский

Если t неприводимо, а s непусто, то s · t непривдимо.

LaTeX

$$For Mul α with IsLeftCancelMul α, (t.Nontrivial) → (s.Nonempty) → (s * t).Nontrivial$$

Lean4

@[to_additive]
theorem mul_left : t.Nontrivial → s.Nonempty → (s * t).Nontrivial :=
  by
  rintro ⟨a, ha, b, hb, hab⟩ ⟨c, hc⟩
  exact ⟨c * a, mul_mem_mul hc ha, c * b, mul_mem_mul hc hb, by simpa⟩

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