IccInclusionRight — Mathlib

English

If x lies in Icc a b, then extending a map on Icc a b to Icc a c by IccExtendCM yields the original value at x; i.e., the extension preserves pointwise values on the left interval.

Русский

Если x ∈ Icc a b, то расширение отображения через IccExtendCM сохраняет значение на x.

LaTeX

$$$\\text{IccExtendCM}_{|}\\text{mem}: \\text{If } x\\in Icc(a,b),\\; IccExtendCM f\!\\; x = f\\langle x, (\\text{hx})\\rangle$$$

Lean4

/-- The embedding into an interval from a sub-interval lying on the right, as a `ContinuousMap`. -/
def IccInclusionRight : C(Icc b c, Icc a c) :=
  .inclusion <| Icc_subset_Icc Fact.out le_rfl

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