iSupLift_inclusion — Mathlib

English

If x ∈ T arises from some i via hx, then iSupLift K dir f hf T hT x = f_i ⟨x, hx⟩.

Русский

Если x ∈ T появилось через i через hx, то iSupLift(K,dir,f,hf,T,hT)(x) = f_i(⟨x, hx⟩).

LaTeX

$$$iSupLift\\ K dir f hf T hT x = f i ⟨x, hx⟩$$$

Lean4

@[simp]
theorem iSupLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) : iSupLift K dir f hf T hT (inclusion h x) = f i x :=
  by
  subst T
  dsimp [iSupLift]
  apply Set.iUnionLift_inclusion
  exact h

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