Nuprl Lemma : term-to-path-is-refl
∀[X:j⊢]. ∀[A:{X ⊢ _}]. ∀a:{X ⊢ _:A}. (X ⊢ <>((a)p) = refl(a) ∈ {X ⊢ _:(Path_A a a)})
Proof
Definitions occuring in Statement :
cubical-refl: refl(a),
term-to-path: <>(a),
path-type: (Path_A a b),
cc-fst: p,
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:A},
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
cubical-refl: refl(a),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
cubical-refl_wf,
cubical_set_cumulativity-i-j,
cubical-type-cumulativity2,
cubical-term_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
lambdaFormation_alt,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
universeIsType,
lambdaEquality_alt,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsTypeImplies,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}a:\{X \mvdash{} \_:A\}. (X \mvdash{} <>((a)p) = refl(a))
Date html generated:
2020_05_20-PM-03_21_10
Last ObjectModification:
2020_04_06-PM-06_38_05
Theory : cubical!type!theory
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