shift_add — Mathlib

English

The leftShiftAddEquiv is an additive equivalence between Cochain K L n and Cochain (K⟦a⟧) L n' when n + a = n'. It is inverse to rightShiftAddEquiv and preserves addition.

Русский

LeftShiftAddEquiv — аддитивная эквиваленция между Cochain(K,L,n) и Cochain(K⟦a⟧,L,n') при условии n + a = n'. Она обратна RightShiftAddEquiv и сохраняет сложение.

LaTeX

$$$\\text{leftShiftAddEquiv}(n,a,n',hn'):\\; \\text{Cochain}(K,L,n) \\simeq_+ \\text{Cochain}(K⟦a⟧,L,n'),\\; \\gamma \\mapsto \\gamma.leftShift a n' hn',\\; \\text{inv}=\\gamma.leftUnshift n hn',$$$

Lean4

@[simp]
theorem shift_add (a : ℤ) : (γ₁ + γ₂).shift a = γ₁.shift a + γ₂.shift a :=
  by
  ext p q hpq
  dsimp
  simp only [shift_v', add_v]

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