proposition: Proposition preserves_binproduct_from_pullback_terminal_unique : isaprop (∑ fg, fg · # F π₁ = f × fg · # F π₂ = g).
proof: Proof. use invproofirrelevance. intros φ₁ φ₂. use subtypePath. { intro. apply isapropdirprod ; apply homset_property. } use (MorphismsIntoPullbackEqual (isPullback_Pullback P)). - exact (pr12 φ₁ @ !(pr12 φ₂)). - exact (pr22 φ₁ @ !(pr22 φ₂)). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.PullbackConstructions UniMath.CategoryTheory.Limits.Preservation UniMath.CategoryTheory.Limits.EquivalencePreservation UniMath.CategoryTheory.Limits.LimitIso UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Equivalences.CompositesAndInverses UniMath.CategoryTheory.whiskering