Nuprl Lemma : csm-ap-term_wf1
∀[Delta,Gamma:j⊢]. ∀[A:{Gamma ⊢j _}]. ∀[s:Delta j⟶ Gamma]. ∀[t:{Gamma ⊢ _:A}]. ((t)s ∈ {Delta ⊢ _:(A)s})
Proof
Definitions occuring in Statement :
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:A},
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
cube_set_map: A ⟶ B,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical-type: {X ⊢ _},
cubical-term: {X ⊢ _:A},
cubical-type-at: A(a),
pi1: fst(t),
all: ∀x:A. B[x],
csm-ap-term: (t)s,
csm-ap-type: (AF)s,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
cubical_type_ap_morph_pair_lemma,
csm-ap_wf,
I_cube_wf,
fset_wf,
nat_wf,
equal_wf,
squash_wf,
true_wf,
istype-universe,
cube-set-restriction_wf,
subtype_rel-equal,
csm-ap-restriction,
subtype_rel_self,
iff_weakening_equal,
names-hom_wf,
cubical-term_wf,
cube_set_map_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
dependent_set_memberEquality_alt,
sqequalRule,
introduction,
extract_by_obid,
dependent_functionElimination,
Error :memTop,
hypothesis,
lambdaEquality_alt,
applyEquality,
hypothesisEquality,
isectElimination,
universeIsType,
lambdaFormation_alt,
instantiate,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
because_Cache,
independent_isectElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination,
inhabitedIsType,
functionIsType,
equalityIstype
Latex:
\mforall{}[Delta,Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{}j \_\}]. \mforall{}[s:Delta j{}\mrightarrow{} Gamma]. \mforall{}[t:\{Gamma \mvdash{} \_:A\}].
((t)s \mmember{} \{Delta \mvdash{} \_:(A)s\})
Date html generated:
2020_05_20-PM-01_53_26
Last ObjectModification:
2020_04_03-PM-08_28_15
Theory : cubical!type!theory
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