Nuprl Lemma : equivTerm_wf
∀[G:j⊢]. ∀[A,B:{G ⊢ _:c𝕌}]. (equivTerm(G;A;B) ∈ {G ⊢ _:c𝕌})
Proof
Definitions occuring in Statement :
equivTerm: equivTerm(G;A;B),
cubical-universe: c𝕌,
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,
equivTerm: equivTerm(G;A;B),
all: ∀x:A. B[x]
Lemmas referenced :
universe-encode_wf,
cubical-equiv_wf,
universe-decode_wf,
equiv-comp_wf,
universe-comp-op_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,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
dependent_functionElimination,
universeIsType,
instantiate
Latex:
\mforall{}[G:j\mvdash{}]. \mforall{}[A,B:\{G \mvdash{} \_:c\mBbbU{}\}]. (equivTerm(G;A;B) \mmember{} \{G \mvdash{} \_:c\mBbbU{}\})
Date html generated:
2020_05_20-PM-07_33_34
Last ObjectModification:
2020_04_28-PM-11_13_52
Theory : cubical!type!theory
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