Nuprl Lemma : ctt-arity_wf
∀[x:CttOp]. (ctt-arity(x) ∈ (ℕ × ℕ) List)
Proof
Definitions occuring in Statement :
ctt-arity: ctt-arity(x),
ctt-op: CttOp,
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
product: x:A × B[x]
Definitions unfolded in proof :
not: ¬A,
false: False,
assert: ↑b,
bnot: ¬bb,
guard: {T},
sq_type: SQType(T),
or: P ∨ Q,
exists: ∃x:A. B[x],
bfalse: ff,
prop: ℙ,
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
subtype_rel: A ⊆r B,
ifthenelse: if b then t else f fi ,
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
implies: P ⇒ Q,
all: ∀x:A. B[x],
ctt-arity: ctt-arity(x),
ctt-op: CttOp,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
ctt-op_wf,
list_wf,
ifthenelse_wf,
nat_wf,
nil_wf,
bool_wf,
btrue_neq_bfalse,
neg_assert_of_eq_atom,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
eqff_to_assert,
ctt-tokens_wf,
l_member_wf,
assert_of_eq_atom,
eqtt_to_assert,
ctt-opid-arity_wf,
eq_atom_wf
Rules used in proof :
productEquality,
cumulativity,
voidElimination,
independent_functionElimination,
instantiate,
dependent_functionElimination,
promote_hyp,
equalityIstype,
dependent_pairFormation_alt,
equalitySymmetry,
equalityTransitivity,
atomEquality,
universeIsType,
setIsType,
lambdaEquality_alt,
independent_isectElimination,
because_Cache,
applyEquality,
equalityElimination,
unionElimination,
lambdaFormation_alt,
inhabitedIsType,
hypothesis,
tokenEquality,
closedConclusion,
hypothesisEquality,
isectElimination,
extract_by_obid,
introduction,
sqequalRule,
rename,
setElimination,
thin,
productElimination,
sqequalHypSubstitution,
cut,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[x:CttOp]. (ctt-arity(x) \mmember{} (\mBbbN{} \mtimes{} \mBbbN{}) List)
Date html generated:
2020_05_20-PM-08_19_29
Last ObjectModification:
2020_03_17-AM-10_36_08
Theory : cubical!type!theory
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