subtype_Icc_eq — Mathlib

English

For a predicate p and LocallyFiniteOrder α, the Icc interval on the subtype equals the subtype of the Icc interval in α: Icc a b = (Icc(a.val, b.val)).subtype p.

Русский

Для предиката p и LocallyFiniteOrder α, интервал Icc на подтипе равен подтипу интервала Icc в α: Icc a b = (Icc(a.val, b.val)).subtype p.

LaTeX

$$$$ \\mathrm{Icc}(a,b) = \\mathrm{subtype}\\ p\\bigl( \\mathrm{Icc}(a.\\mathrm{val}, b.\\mathrm{val}) \\bigr). $$$$

Lean4

theorem subtype_Icc_eq : Icc a b = (Icc (a : α) b).subtype p :=
  rfl

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