eq — Mathlib · SciLib

English

Equality on a type is primitive recursive.

Русский

Равенство на типе является примитивно вычисимой relation.

LaTeX

$$$\\text{Equality on }\\alpha\\text{ is primitive recursive}$$$

Lean4

protected theorem eq : PrimrecRel (@Eq α) :=
  have : PrimrecRel fun a b : ℕ => a = b :=
    (PrimrecPred.and nat_le nat_le.swap).of_eq fun a => by simp [le_antisymm_iff]
  (this.decide.comp₂ (Primrec.encode.comp₂ Primrec₂.left) (Primrec.encode.comp₂ Primrec₂.right)).primrecRel.of_eq
    fun _ _ => encode_injective.eq_iff

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