Nuprl Lemma : ctt-type-meaning1_wf
∀[X:⊢''']. (ctt-type-meaning1{i:l}(X) ∈ 𝕌{i''''})
Proof
Definitions occuring in Statement :
ctt-type-meaning1: ctt-type-meaning1{i:l}(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-type-meaning1: ctt-type-meaning1{i:l}(X),
nat: ℕ,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than: a < b,
squash: ↓T,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
prop: ℙ
Lemmas referenced :
int_seg_wf,
ctt-level-type_wf,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
istype-le,
top_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
cumulativity,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
hypothesisEquality,
dependent_set_memberEquality_alt,
setElimination,
rename,
productElimination,
imageElimination,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
Error :memTop,
independent_pairFormation,
universeIsType,
voidElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
instantiate
Latex:
\mforall{}[X:\mvdash{}''']. (ctt-type-meaning1\{i:l\}(X) \mmember{} \mBbbU{}\{i''''\})
Date html generated:
2020_05_20-PM-07_55_44
Last ObjectModification:
2020_05_05-AM-09_39_39
Theory : cubical!type!theory
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