Nuprl Lemma : ctt-level-type_wf
∀[X:⊢''']. ∀[lvl:ℕ]. (X ⊢lvl ∈ 𝕌{i''''})
Proof
Definitions occuring in Statement :
ctt-level-type: {X ⊢lvl _},
cubical_set: CubicalSet,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ctt-level-type: {X ⊢lvl _},
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
false: False
Lemmas referenced :
eq_int_wf,
uiff_transitivity,
equal-wf-base,
bool_wf,
set_subtype_base,
le_wf,
istype-int,
int_subtype_base,
assert_wf,
eqtt_to_assert,
assert_of_eq_int,
cubical-type_wf,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
istype-assert,
istype-void,
istype-nat,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
natural_numberEquality,
inhabitedIsType,
lambdaFormation_alt,
unionElimination,
equalityElimination,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
intEquality,
lambdaEquality_alt,
independent_isectElimination,
because_Cache,
independent_functionElimination,
productElimination,
instantiate,
independent_pairFormation,
equalityIstype,
sqequalBase,
equalitySymmetry,
functionIsType,
voidElimination,
equalityTransitivity,
dependent_functionElimination,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[X:\mvdash{}''']. \mforall{}[lvl:\mBbbN{}]. (X \mvdash{}lvl \mmember{} \mBbbU{}\{i''''\})
Date html generated:
2020_05_20-PM-07_45_24
Last ObjectModification:
2020_05_04-AM-09_53_54
Theory : cubical!type!theory
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