Nuprl Lemma : ctt-term-meaning_wf
∀[X:⊢''']. (cttTerm(X) ∈ 𝕌{i''''})
Proof
Definitions occuring in Statement :
ctt-term-meaning: cttTerm(X),
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ctt-term-meaning: cttTerm(X),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q
Lemmas referenced :
int_seg_wf,
ctt-level-type_wf,
int_seg_subtype_nat,
istype-false,
cubical-term_wf-level-type,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
closedConclusion,
natural_numberEquality,
hypothesis,
applyEquality,
lambdaEquality_alt,
cumulativity,
hypothesisEquality,
universeIsType,
universeEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation_alt,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
instantiate
Latex:
\mforall{}[X:\mvdash{}''']. (cttTerm(X) \mmember{} \mBbbU{}\{i''''\})
Date html generated:
2020_05_20-PM-07_50_08
Last ObjectModification:
2020_05_05-AM-09_33_41
Theory : cubical!type!theory
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