Mathlib Map

Theorems · Definition

Equiv.sigmaOptionEquivOfSome

{α : Type u_9} → (p : Option α → Type v) → (∀ (a : p none), False) → (x : Option α) × p x ≃ (x : α) × p (some x)

A sigma type over an Option is equivalent to the sigma set over the original type, if the fiber is empty at none.

Defined in
Mathlib.Logic.Equiv.Basic
Cited by
0 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Quot.sound
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Around this declaration

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derangements.derangementsOptionEquivSigmaAtMostOneFixedPoint · cited by 0derangements.derangements…Equiv · cited by 8337EquivEquiv.symm · cited by 3681Equiv.symmEquiv.trans · cited by 337Equiv.transEquiv.optionIsSomeEquiv · cited by 3Equiv.optionIsSomeEquivEquiv.sigmaCongrLeft' · cited by 3Equiv.sigmaCongrLeft'Equiv.sigmaSubtypeEquivOfSubset · cited by 0Equiv.sigmaSubtypeEquivOf…Equiv.sigmaOptionEquivOfSomeCITED BYCITES

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