Nuprl Lemma : closed-cubical-term_wf
∀[T:{ * ⊢ _}]. (closed-cubical-term(T) ∈ Type)
Proof
Definitions occuring in Statement :
closed-cubical-term: closed-cubical-term(T),
closed-cubical-type: { * ⊢ _},
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
closed-cubical-term: closed-cubical-term(T),
closed-cubical-type: { * ⊢ _},
pi1: fst(t),
so_lambda: λ2x.t[x],
pi2: snd(t),
subtype_rel: A ⊆r B,
so_apply: x[s],
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
fset_wf,
nat_wf,
all_wf,
names-hom_wf,
equal_wf,
subtype_rel_self,
closed-cubical-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
setEquality,
functionEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
setElimination,
rename,
productElimination,
applyEquality,
hypothesisEquality,
because_Cache,
lambdaEquality_alt,
universeIsType,
inhabitedIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[T:\{ * \mvdash{} \_\}]. (closed-cubical-term(T) \mmember{} Type)
Date html generated:
2020_05_20-PM-01_52_50
Last ObjectModification:
2020_03_20-PM-00_34_50
Theory : cubical!type!theory
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