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Theorems · Definition

Equiv.sigmaCongrLeft

{α₁ : Type u_1} → {α₂ : Type u_2} → {β : α₂ → Type u_3} → (e : α₁ ≃ α₂) → (a : α₁) × β (e a) ≃ (a : α₂) × β a

An equivalence f : α₁ ≃ α₂ generates an equivalence between Σ a, β (f a) and Σ a, β a.

Defined in
Mathlib.Logic.Equiv.Defs
Cited by
2 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Equiv.sigmaCongr · cited by 4Equiv.sigmaCongrEquiv.sigmaCongrLeft' · cited by 3Equiv.sigmaCongrLeft'Equiv.sigmaCongrLeft_apply · cited by 0Equiv.sigmaCongrLeft_applyfinSigmaFinEquiv.eq_def · cited by 0finSigmaFinEquiv.eq_defDFunLike.coe · cited by 62936DFunLike.coeEquiv · cited by 8337EquivEquiv.symm · cited by 3681Equiv.symmEquiv.sigmaCongrLeftCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.