Nuprl Lemma : cubical-term-sq-presheaf-term
∀[X,A:Top]. ({X ⊢ _:A} ~ {X ⊢ _:A})
Proof
Definitions occuring in Statement :
cubical-term: {X ⊢ _:A},
cube-cat: CubeCat,
presheaf-term: {X ⊢ _:A},
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical-term: {X ⊢ _:A},
presheaf-term: {X ⊢ _:A},
cube-cat: CubeCat,
all: ∀x:A. B[x],
top: Top,
I_cube: A(I),
I_set: A(I),
cubical-type-at: A(a),
presheaf-type-at: A(a),
cube-set-restriction: f(s),
psc-restriction: f(s),
cubical-type-ap-morph: (u a f),
presheaf-type-ap-morph: (u a f)
Lemmas referenced :
cat_ob_pair_lemma,
cat_arrow_triple_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[X,A:Top]. (\{X \mvdash{} \_:A\} \msim{} \{X \mvdash{} \_:A\})
Date html generated:
2018_05_23-AM-08_45_25
Last ObjectModification:
2018_05_20-PM-05_55_33
Theory : cubical!type!theory
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