Nuprl Lemma : mk-ctt-term-mng_wf
∀[X:⊢''']. ∀[lvl:ℕ4]. ∀[T:{X ⊢lvl _}]. ∀[t:{X ⊢ _:T}]. (mk-ctt-term-mng(lvl; T; t) ∈ cttTerm(X))
Proof
Definitions occuring in Statement :
mk-ctt-term-mng: mk-ctt-term-mng(lvl; T; t),
ctt-term-meaning: cttTerm(X),
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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mk-ctt-term-mng: mk-ctt-term-mng(lvl; T; t),
ctt-term-meaning: cttTerm(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 :
cubical-term_wf-level-type,
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,
int_seg_wf,
cubical_set_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
universeIsType,
dependent_set_memberEquality_alt,
setElimination,
rename,
productElimination,
imageElimination,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
Error :memTop,
sqequalRule,
independent_pairFormation,
voidElimination,
instantiate,
dependent_pairEquality_alt,
because_Cache,
productIsType
Latex:
\mforall{}[X:\mvdash{}''']. \mforall{}[lvl:\mBbbN{}4]. \mforall{}[T:\{X \mvdash{}lvl \_\}]. \mforall{}[t:\{X \mvdash{} \_:T\}]. (mk-ctt-term-mng(lvl; T; t) \mmember{} cttTerm(X))
Date html generated:
2020_05_20-PM-07_54_25
Last ObjectModification:
2020_05_05-AM-11_51_34
Theory : cubical!type!theory
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