Nuprl Lemma : sigma-unelim-elim

[X:j⊢]. ∀[A:{X ⊢ _}]. ∀[B:{X.A ⊢ _}].  (SigmaElim SigmaUnElim 1(X.A.B) ∈ X.A.B ij⟶ X.A.B)


Proof




Definitions occuring in Statement :  sigma-unelim-csm: SigmaUnElim sigma-elim-csm: SigmaElim cubical-sigma: Σ B cube-context-adjoin: X.A cubical-type: {X ⊢ _} csm-id: 1(X) csm-comp: F cube_set_map: A ⟶ B cubical_set: CubicalSet uall: [x:A]. B[x] equal: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T cubical_set: CubicalSet cube-context-adjoin: X.A psc-adjoin: X.A I_cube: A(I) I_set: A(I) cubical-type-at: A(a) presheaf-type-at: A(a) cube-set-restriction: f(s) psc-restriction: f(s) cubical-type-ap-morph: (u f) presheaf-type-ap-morph: (u f) cube_set_map: A ⟶ B csm-comp: F pscm-comp: F sigma-elim-csm: SigmaElim sigma-elim-pscm: SigmaElim cc-adjoin-cube: (v;u) psc-adjoin-set: (v;u) sigma-unelim-csm: SigmaUnElim sigma-unelim-pscm: SigmaUnElim csm-id: 1(X) pscm-id: 1(X)
Lemmas referenced :  ps-sigma-unelim-elim cube-cat_wf cubical-type-sq-presheaf-type
Rules used in proof :  cut introduction extract_by_obid sqequalHypSubstitution sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isectElimination thin hypothesis sqequalRule Error :memTop

Latex:
\mforall{}[X:j\mvdash{}].  \mforall{}[A:\{X  \mvdash{}  \_\}].  \mforall{}[B:\{X.A  \mvdash{}  \_\}].    (SigmaElim  o  SigmaUnElim  =  1(X.A.B))



Date html generated: 2020_05_20-PM-02_28_12
Last ObjectModification: 2020_04_04-AM-09_26_03

Theory : cubical!type!theory


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