restrictionGEIso — Mathlib

English

The integer type inherits right-cancellation: a + b = a + c implies b = c.

Русский

Целые числа удовлетворяют правому cancellation: если a+b = a+c, то b=c.

LaTeX

$$IsRightCancelInt$$

Lean4

/-- If `h : ConnectData K L`, then `h.cochainComplex` identifies to `L` in degrees `≥ 0`. -/
@[simps!]
def restrictionGEIso : h.cochainComplex.restriction (ComplexShape.embeddingUpIntGE 0) ≅ L :=
  Hom.isoOfComponents
    (fun n ↦ h.cochainComplex.restrictionXIso (ComplexShape.embeddingUpIntGE 0) (i := n) (i' := n) (by simp))
    (by
      rintro n _ rfl
      dsimp only
      rw [restriction_d_eq (e := (ComplexShape.embeddingUpIntGE 0)) _ (i' := n) (j' := (n + 1 : ℕ)) (by simp) (by simp),
        cochainComplex_d, h.d_ofNat]
      simp)

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