coe_set_mk — Mathlib

English

The carrier set of mk from a.Subsemiring is exactly that Subsemiring, i.e., the coe to Set of mk equals the Subsemiring.

Русский

Образ прямого переноса mk для подп Semiring равен именно этому подп Semiring по множеству носителя.

LaTeX

$$$ (\\mathrm{mk} \\\\ toSubsemiring \\\\ eq\\_zero\\_of\\_mem\\_of\\_neg\\_mem : \\mathrm{Set} \\, R) = toSubsemiring. $$$

Lean4

@[simp]
theorem coe_set_mk {R : Type*} [Ring R] {toSubsemiring : Subsemiring R} (eq_zero_of_mem_of_neg_mem) :
    (mk toSubsemiring eq_zero_of_mem_of_neg_mem : Set R) = toSubsemiring :=
  rfl

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