Nuprl Lemma : transEquiv-trans_wf
∀[G:j⊢]. ∀[A,B:{G ⊢ _:c𝕌}]. ∀[p:{G ⊢ _:(Path_c𝕌 A B)}]. (transEquivFun(p) ∈ {G ⊢ _:(decode(A) ⟶ decode(B))})
Proof
Definitions occuring in Statement :
transEquiv-trans: transEquivFun(p),
universe-decode: decode(t),
cubical-universe: c𝕌,
path-type: (Path_A a b),
cubical-fun: (A ⟶ B),
cubical-term: {X ⊢ _:A},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
transEquiv-trans: transEquivFun(p),
all: ∀x:A. B[x]
Lemmas referenced :
equiv-fun_wf,
universe-decode_wf,
transEquiv_wf,
istype-cubical-term,
path-type_wf,
cubical-universe_wf,
istype-cubical-universe-term,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
instantiate,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
dependent_functionElimination,
universeIsType
Latex:
\mforall{}[G:j\mvdash{}]. \mforall{}[A,B:\{G \mvdash{} \_:c\mBbbU{}\}]. \mforall{}[p:\{G \mvdash{} \_:(Path\_c\mBbbU{} A B)\}].
(transEquivFun(p) \mmember{} \{G \mvdash{} \_:(decode(A) {}\mrightarrow{} decode(B))\})
Date html generated:
2020_05_20-PM-07_34_43
Last ObjectModification:
2020_05_01-AM-09_52_15
Theory : cubical!type!theory
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