Nuprl Lemma : unit-path-type
∀[G:j⊢]. ∀[x,y:{G ⊢ _:1}]. ∀a,b:{G ⊢ _:(Path_1 x y)}. (a = b ∈ {G ⊢ _:(Path_1 x y)})
Proof
Definitions occuring in Statement :
path-type: (Path_A a b),
cubical-unit: 1,
cubical-term: {X ⊢ _:A},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a
Lemmas referenced :
paths-equal,
cubical-unit_wf,
path-type-subtype,
cubical-term_wf,
path-type_wf,
cubical_set_wf,
unit-pathtype
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
lambdaFormation_alt,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
independent_isectElimination,
inhabitedIsType,
universeIsType,
instantiate,
lambdaEquality_alt,
dependent_functionElimination,
axiomEquality,
functionIsTypeImplies,
isect_memberEquality_alt,
isectIsTypeImplies,
because_Cache
Latex:
\mforall{}[G:j\mvdash{}]. \mforall{}[x,y:\{G \mvdash{} \_:1\}]. \mforall{}a,b:\{G \mvdash{} \_:(Path\_1 x y)\}. (a = b)
Date html generated:
2020_05_20-PM-03_34_49
Last ObjectModification:
2020_04_06-PM-06_59_59
Theory : cubical!type!theory
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