Nuprl Lemma : cubical-pi_wf

[X:j⊢]. ∀[A:{X ⊢ _}]. ∀[B:{X.A ⊢ _}].  X ⊢ ΠB


Proof




Definitions occuring in Statement :  cubical-pi: ΠB cube-context-adjoin: X.A cubical-type: {X ⊢ _} cubical_set: CubicalSet uall: [x:A]. B[x] member: 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) cubical-pi: ΠB presheaf-pi: ΠB cubical-pi-family: cubical-pi-family(X;A;B;I;a) presheaf-pi-family: presheaf-pi-family(C; X; A; B; I; a) cube-cat: CubeCat all: x:A. B[x] cc-adjoin-cube: (v;u) psc-adjoin-set: (v;u)
Lemmas referenced :  presheaf-pi_wf cube-cat_wf cubical-type-sq-presheaf-type cat_ob_pair_lemma cat_arrow_triple_lemma cat_comp_tuple_lemma
Rules used in proof :  cut introduction extract_by_obid sqequalHypSubstitution sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isectElimination thin hypothesis sqequalRule Error :memTop,  dependent_functionElimination

Latex:
\mforall{}[X:j\mvdash{}].  \mforall{}[A:\{X  \mvdash{}  \_\}].  \mforall{}[B:\{X.A  \mvdash{}  \_\}].    X  \mvdash{}  \mPi{}A  B



Date html generated: 2020_05_20-PM-02_00_06
Last ObjectModification: 2020_04_03-PM-08_33_13

Theory : cubical!type!theory


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