Nuprl Lemma : same-cubical-type-trivial_1
∀[X:j⊢]. ∀[i:{X ⊢ _:𝕀}]. ∀[x,y,B:Top]. X, (i=0), (i=1) ⊢ x=y:B
Proof
Definitions occuring in Statement :
same-cubical-term: X ⊢ u=v:A,
context-subset: Gamma, phi,
face-zero: (i=0),
face-one: (i=1),
interval-type: 𝕀,
cubical-term: {X ⊢ _:A},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
top: Top
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
same-cubical-term: X ⊢ u=v:A
Lemmas referenced :
empty-context-subset-lemma3',
istype-top,
cubical-term_wf,
interval-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
axiomEquality,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType,
instantiate
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[i:\{X \mvdash{} \_:\mBbbI{}\}]. \mforall{}[x,y,B:Top]. X, (i=0), (i=1) \mvdash{} x=y:B
Date html generated:
2020_05_20-PM-04_14_07
Last ObjectModification:
2020_04_10-AM-04_42_37
Theory : cubical!type!theory
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