Nuprl Lemma : cc-snd_wf
∀[Gamma:CubicalSet]. ∀[A:{Gamma ⊢ _}]. (q ∈ {Gamma.A ⊢ _:(A)p})
Proof
Definitions occuring in Statement :
cc-snd: q,
cc-fst: p,
cube-context-adjoin: X.A,
cubical-term: {X ⊢ _:AF},
csm-ap-type: (AF)s,
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-term: {X ⊢ _:AF},
prop: ℙ,
so_apply: x[s],
so_lambda: λ2x.t[x],
and: P ∧ Q,
functor-ob: ob(F),
subtype_rel: A ⊆r B,
cube-set-restriction: f(s),
pi2: snd(t),
cubical-type-at: A(a),
csm-ap: (s)x,
pi1: fst(t),
top: Top,
all: ∀x:A. B[x],
I-cube: X(I),
cube-context-adjoin: X.A,
csm-ap-type: (AF)s,
cc-fst: p,
cc-snd: q,
cubical-set: CubicalSet,
cubical-type: {X ⊢ _},
cubical-type-ap-morph: (u a f),
name-morph: name-morph(I;J)
Lemmas referenced :
cubical-type_wf,
cubical-set_wf,
id-morph_wf,
equal-wf-T-base,
compose_wf,
name-comp_wf,
equal_wf,
all_wf,
name-morph_wf,
I-cube_wf,
subtype_rel_self,
coordinate_name_wf,
list_wf,
ob_pair_lemma,
cube-context-adjoin_wf,
istype-void
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
dependent_set_memberEquality_alt,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
baseClosed,
spreadEquality,
functionEquality,
dependent_pairEquality,
dependent_set_memberEquality,
because_Cache,
functionExtensionality,
applyEquality,
productEquality,
lambdaEquality,
voidEquality,
voidElimination,
isect_memberEquality,
dependent_functionElimination,
productElimination,
rename,
setElimination,
lambdaFormation,
dependent_pairEquality_alt
Latex:
\mforall{}[Gamma:CubicalSet]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. (q \mmember{} \{Gamma.A \mvdash{} \_:(A)p\})
Date html generated:
2019_11_05-PM-00_26_06
Last ObjectModification:
2018_11_08-PM-00_51_28
Theory : cubical!sets
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