Nuprl Lemma : cubical-type-sq-presheaf-type
∀[X:Top]. ({X ⊢ _} ~ {X ⊢ _})
Proof
Definitions occuring in Statement :
cubical-type: {X ⊢ _},
cube-cat: CubeCat,
presheaf-type: {X ⊢ _},
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical-type: {X ⊢ _},
presheaf-type: {X ⊢ _},
cube-cat: CubeCat,
all: ∀x:A. B[x],
top: Top,
I_cube: A(I),
I_set: A(I),
cube-set-restriction: f(s),
psc-restriction: f(s)
Lemmas referenced :
cat_ob_pair_lemma,
cat_arrow_triple_lemma,
cat_id_tuple_lemma,
cat_comp_tuple_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
Latex:
\mforall{}[X:Top]. (\{X \mvdash{} \_\} \msim{} \{X \mvdash{} \_\})
Date html generated:
2018_05_23-AM-08_41_29
Last ObjectModification:
2018_05_20-PM-05_51_32
Theory : cubical!type!theory
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