Nuprl Lemma : csm-cubical-bool
∀[H:j⊢]. ∀[s:H j⟶ ()]. ((Bool)s = Bool ∈ {H ⊢ _:c𝕌})
Proof
Definitions occuring in Statement :
cubical-bool: Bool,
cubical-universe: c𝕌,
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:A},
cube_set_map: A ⟶ B,
trivial-cube-set: (),
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
cubical-bool: Bool,
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
squash: ↓T,
all: ∀x:A. B[x],
true: True,
discrete-comp: discrete-comp(G;T),
csm-composition: (comp)sigma,
universe-encode: encode(T;cT)
Lemmas referenced :
cube_set_map_wf,
trivial-cube-set_wf,
cubical_set_wf,
csm-universe-encode,
discrete-cubical-type_wf,
bool_wf,
discrete-comp_wf,
equal_wf,
squash_wf,
true_wf,
istype-universe,
cubical-term_wf-universe,
csm-discrete-cubical-type,
universe-encode_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
hypothesis,
universeIsType,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType,
instantiate,
hyp_replacement,
equalitySymmetry,
applyEquality,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
universeEquality,
dependent_functionElimination,
Error :memTop,
natural_numberEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[H:j\mvdash{}]. \mforall{}[s:H j{}\mrightarrow{} ()]. ((Bool)s = Bool)
Date html generated:
2020_05_20-PM-07_44_54
Last ObjectModification:
2020_05_02-PM-08_06_20
Theory : cubical!type!theory
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