Nuprl Lemma : context-subset-term-iota
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}]. ∀[phi:{Gamma ⊢ _:𝔽}]. ∀[v:{Gamma, phi ⊢ _:A}]. ((v)iota = v ∈ {Gamma, phi ⊢ _:A})
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
face-type: 𝔽,
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:A},
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,
subtype_rel: A ⊆r B,
guard: {T},
cubical-term: {X ⊢ _:A},
subset-iota: iota,
csm-ap-term: (t)s,
csm-ap: (s)x,
uimplies: b supposing a
Lemmas referenced :
cubical-term_wf,
context-subset_wf,
thin-context-subset,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
face-type_wf,
cubical-type_wf,
cubical_set_wf,
cubical-term-equal,
I_cube_wf,
fset_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
equalitySymmetry,
universeIsType,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
equalityTransitivity,
applyEquality,
sqequalRule,
setElimination,
rename,
functionExtensionality,
independent_isectElimination,
because_Cache
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[phi:\{Gamma \mvdash{} \_:\mBbbF{}\}]. \mforall{}[v:\{Gamma, phi \mvdash{} \_:A\}]. ((v)iota = v)
Date html generated:
2020_05_20-PM-04_08_37
Last ObjectModification:
2020_04_10-AM-03_50_33
Theory : cubical!type!theory
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