Nuprl Lemma : cubical-term_wf-level-type
∀[X:⊢''']. ∀[lvl:ℕ4]. ∀[T:{X ⊢lvl _}]. ({X ⊢ _:T} ∈ 𝕌{i''''})
Proof
Definitions occuring in Statement :
ctt-level-type: {X ⊢lvl _}
,
cubical-term: {X ⊢ _:A}
,
cubical_set: CubicalSet
,
int_seg: {i..j-}
,
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
natural_number: $n
,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
all: ∀x:A. B[x]
,
int_seg: {i..j-}
,
lelt: i ≤ j < k
,
and: P ∧ Q
,
le: A ≤ B
,
decidable: Dec(P)
,
or: P ∨ Q
,
uimplies: b supposing a
,
sq_type: SQType(T)
,
implies: P
⇒ Q
,
guard: {T}
,
ctt-level-type: {X ⊢lvl _}
,
eq_int: (i =z j)
,
ifthenelse: if b then t else f fi
,
btrue: tt
,
bfalse: ff
,
not: ¬A
,
satisfiable_int_formula: satisfiable_int_formula(fmla)
,
exists: ∃x:A. B[x]
,
false: False
,
prop: ℙ
,
nat: ℕ
,
less_than: a < b
,
squash: ↓T
Lemmas referenced :
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
int_seg_properties,
cubical-term-eqcd,
int_seg_subtype_special,
int_seg_cases,
full-omega-unsat,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
ctt-level-type_wf,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
istype-le,
int_seg_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
because_Cache,
hypothesis,
productElimination,
unionElimination,
instantiate,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
hypothesisEquality,
sqequalRule,
hypothesis_subsumption,
approximateComputation,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
Error :memTop,
independent_pairFormation,
universeIsType,
voidElimination,
dependent_set_memberEquality_alt,
imageElimination
Latex:
\mforall{}[X:\mvdash{}''']. \mforall{}[lvl:\mBbbN{}4]. \mforall{}[T:\{X \mvdash{}lvl \_\}]. (\{X \mvdash{} \_:T\} \mmember{} \mBbbU{}\{i''''\})
Date html generated:
2020_05_20-PM-07_48_18
Last ObjectModification:
2020_05_04-AM-09_45_08
Theory : cubical!type!theory
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