head_desc — Mathlib

English

As above, in the dual formulation: if ∀ j, ι arrows j ≫ g = fs j and head arrows ≫ g = f, then g = desc f fs w.

Русский

Как выше, но в двойственной формулировке: если ∀ j, ι arrows j ≫ g = fs j и head arrows ≫ g = f, то g = desc f fs w.

LaTeX

$$$\\forall j:\\, J,\\ ι arrows j \\circ g = fs j \\implies head arrows \\circ g = f \\implies g = \\mathrm{desc}(f,fs,w).$$$

Lean4

@[reassoc]
theorem head_desc : head arrows ≫ desc f fs w = f := by
  simp only [colimit.ι_desc, WidePushoutShape.mkCocone_pt, WidePushoutShape.mkCocone_ι_app]

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