Share the proofs of ×-comm and ⊎-comm of type isomorphisms and add a pairing operation #2868
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JacquesCarette
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Nov 11, 2025
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JacquesCarette
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I was afraid (from the description) that this might make a mess of the dependency graph. But it seems not - great.
So this looks like a nice simplification.
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The functions
Function.Related.TypeIsomorphism.⊎-commandData.Sum.Properties.swap-↔are the same, thus this PR points one to the other.Function.Related.TypeIsomorphism.∃∃↔∃∃is similar as well.To make things parallel, this PR keeps only the name of
Function.Related.TypeIsomorphism.×-command moves its implementation toData.Product.Properties.Finally, this PR adds
_,′-↔_ : A ↔ C → B ↔ D → (A × B) ↔ (C × D)that pairs two type isomorphisms.(The type of
_,′-↔_can't be expressed as_×_ Preserves₂ _↔_ ⟶ _↔_ ⟶ _↔_because that requiresAandCto have identicalLevels and similarlyBandDwould need to have the sameLevel.)