Nuprl Lemma : cubical-id-fun_wf

[X:j⊢]. ∀[A:{X ⊢ _}].  (cubical-id-fun(X) ∈ {X ⊢ _:(A ⟶ A)})


Proof




Definitions occuring in Statement :  cubical-id-fun: cubical-id-fun(X) cubical-fun: (A ⟶ B) cubical-term: {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 cubical-fun: (A ⟶ B) presheaf-fun: (A ⟶ B) cubical-fun-family: cubical-fun-family(X; A; B; I; a) presheaf-fun-family: presheaf-fun-family(C; X; A; B; I; a) cube-cat: CubeCat all: x:A. B[x] 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-id-fun: cubical-id-fun(X) presheaf-id-fun: presheaf-id-fun(X) cubical-lam: cubical-lam(X;b) presheaf-lam: presheaf-lam(X;b) cubical-lambda: b) presheaf-lambda: b) cc-snd: q psc-snd: q cc-adjoin-cube: (v;u) psc-adjoin-set: (v;u)
Lemmas referenced :  presheaf-id-fun_wf cube-cat_wf cubical-type-sq-presheaf-type cat_ob_pair_lemma cat_arrow_triple_lemma cat_comp_tuple_lemma cubical-term-sq-presheaf-term
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{}  \_\}].    (cubical-id-fun(X)  \mmember{}  \{X  \mvdash{}  \_:(A  {}\mrightarrow{}  A)\})



Date html generated: 2020_05_20-PM-02_25_16
Last ObjectModification: 2020_04_03-PM-08_35_25

Theory : cubical!type!theory


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