Nuprl Lemma : subset-iota-is-id
∀[H:j⊢]. ∀[phi:{H ⊢ _:𝔽}]. ∀[v:{H, phi ⊢ _}]. (v = (v)iota ∈ {H, 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,
and: P ∧ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
cubical-type_wf,
context-subset_wf,
cubical-term_wf,
face-type_wf,
cubical_set_wf,
cubical-type-equal,
I_cube_wf,
fset_wf,
nat_wf,
names-hom_wf,
cube-set-restriction_wf,
eta_conv
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
instantiate,
independent_isectElimination,
setElimination,
rename,
productElimination,
sqequalRule,
dependent_pairEquality_alt,
lambdaEquality_alt,
applyEquality,
because_Cache,
functionIsType,
functionExtensionality_alt,
equalitySymmetry,
cumulativity,
universeEquality,
functionExtensionality
Latex:
\mforall{}[H:j\mvdash{}]. \mforall{}[phi:\{H \mvdash{} \_:\mBbbF{}\}]. \mforall{}[v:\{H, phi \mvdash{} \_\}]. (v = (v)iota)
Date html generated:
2020_05_20-PM-04_08_24
Last ObjectModification:
2020_04_10-AM-03_50_05
Theory : cubical!type!theory
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