lift_unique — Mathlib

English

For all x,y ∈ M×S, equality of lifts corresponds to swapped products under g.

Русский

Для всех x,y ∈ M×S равенство подъемов соответствует обмену произведений под g.

LaTeX

$$$ f.lift hg (f.mk' x.1 x.2) = f.lift hg (f.mk' y.1 y.2) \iff g(x.1 \cdot y.2) = g(y.1 \cdot x.2) $$$

Lean4

@[to_additive]
theorem lift_unique {j : N →* P} (hj : ∀ x, j (f x) = g x) : f.lift hg = j :=
  by
  ext
  rw [lift_spec, ← hj, ← hj, ← j.map_mul]
  apply congr_arg
  rw [← sec_spec']

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