Nuprl Lemma : context-subset-ap-iota
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}]. ∀[phi:{Gamma ⊢ _:𝔽}]. ((A)iota = A ∈ {Gamma, phi ⊢ _})
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
face-type: 𝔽,
cubical-term: {X ⊢ _:A},
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
subset-iota: iota,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
cubical-type: {X ⊢ _},
subset-iota: iota,
csm-ap-type: (AF)s,
csm-ap: (s)x,
context-subset: Gamma, phi,
all: ∀x:A. B[x]
Lemmas referenced :
cubical-type-equal2,
context-subset_wf,
csm-ap-type_wf,
subset-iota_wf2,
thin-context-subset,
cubical-term_wf,
face-type_wf,
cubical-type_wf,
cubical_set_wf,
I_cube_wf,
fset_wf,
nat_wf,
I_cube_pair_redex_lemma,
names-hom_wf,
cube_set_restriction_pair_lemma,
cube-set-restriction_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
universeIsType,
instantiate,
setElimination,
rename,
productElimination,
sqequalRule,
dependent_pairEquality_alt,
functionExtensionality,
dependent_functionElimination,
Error :memTop,
applyEquality,
because_Cache,
functionIsType
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[phi:\{Gamma \mvdash{} \_:\mBbbF{}\}]. ((A)iota = A)
Date html generated:
2020_05_20-PM-04_08_10
Last ObjectModification:
2020_04_10-AM-03_49_33
Theory : cubical!type!theory
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