prodMap_id_id — Mathlib

English

The product of identity partial functions is the identity on the product type: (id α) × (id β) = id (Prod α β).

Русский

Произведение идентичности частичных функций равно идентичности на произведении: id α × id β = id (Prod α β).

LaTeX

$$$$ (\\mathrm{id}\\,\\alpha) \\prodMap (\\mathrm{id}\\,\\beta) = \\mathrm{id}\\, (\\mathrm{Prod}\\, \\alpha\\, \\beta). $$$$

Lean4

@[simp]
theorem prodMap_id_id : (PFun.id α).prodMap (PFun.id β) = PFun.id _ := by aesop

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