Nuprl Lemma : csm-same-cubical-term
∀[X:j⊢]. ∀[A:{X ⊢ _}]. ∀[u,v:{X ⊢ _:A}]. ∀[Y:j⊢]. ∀[s:Y j⟶ X]. Y ⊢ (u)s=(v)s:(A)s supposing X ⊢ u=v:A
Proof
Definitions occuring in Statement :
same-cubical-term: X ⊢ u=v:A,
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:A},
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
cube_set_map: A ⟶ B,
cubical_set: CubicalSet,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
same-cubical-term: X ⊢ u=v:A,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
true: True
Lemmas referenced :
csm-ap-term_wf,
squash_wf,
true_wf,
cubical-term_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
cube_set_map_wf,
cubical-type_wf,
same-cubical-term_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
applyEquality,
thin,
lambdaEquality_alt,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeIsType,
instantiate,
sqequalRule,
inhabitedIsType,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[u,v:\{X \mvdash{} \_:A\}]. \mforall{}[Y:j\mvdash{}]. \mforall{}[s:Y j{}\mrightarrow{} X].
Y \mvdash{} (u)s=(v)s:(A)s supposing X \mvdash{} u=v:A
Date html generated:
2020_05_20-PM-03_00_12
Last ObjectModification:
2020_04_04-PM-05_14_57
Theory : cubical!type!theory
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