Nuprl Lemma : cubical-term_wf
∀[X:CubicalSet]. ∀[A:{X ⊢ _}]. ({X ⊢ _:A} ∈ Type)
Proof
Definitions occuring in Statement :
cubical-term: {X ⊢ _:AF},
cubical-type: {X ⊢ _},
cubical-set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical-type: {X ⊢ _},
cubical-term: {X ⊢ _:AF},
pi1: fst(t),
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
list_wf,
coordinate_name_wf,
I-cube_wf,
all_wf,
name-morph_wf,
equal_wf,
cube-set-restriction_wf,
cubical-type_wf,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
setEquality,
functionEquality,
lemma_by_obid,
isectElimination,
hypothesis,
hypothesisEquality,
applyEquality,
because_Cache,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[A:\{X \mvdash{} \_\}]. (\{X \mvdash{} \_:A\} \mmember{} Type)
Date html generated:
2016_06_16-PM-05_39_58
Last ObjectModification:
2015_12_28-PM-04_35_52
Theory : cubical!sets
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