bit_cases_on_inj — Mathlib

English

The equivalence (fun n => bitCasesOn n H1) = (fun n => bitCasesOn n H2) is equivalent to H1 = H2.

Русский

Эквивалентность функций (путь) равенства bitCasesOn равна эквивалентности H1 = H2.

LaTeX

$$$$ (\, (\forall n, \text{bitCasesOn}(n,H_1) = \text{bitCasesOn}(n,H_2)) ) \iff H_1 = H_2. $$$$

Lean4

@[simp]
theorem bit_cases_on_inj {motive : ℕ → Sort u} (H₁ H₂ : ∀ b n, motive (bit b n)) :
    ((fun n => bitCasesOn n H₁) = fun n => bitCasesOn n H₂) ↔ H₁ = H₂ :=
  bit_cases_on_injective.eq_iff

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