Nuprl Lemma : ctt-opid-arity_wf
∀[t:Atom]. (ctt-opid-arity(t) ∈ (ℕ × ℕ) List)
Proof
Definitions occuring in Statement :
ctt-opid-arity: ctt-opid-arity(t),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
product: x:A × B[x],
atom: Atom
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ctt-opid-arity: ctt-opid-arity(t),
subtype_rel: A ⊆r B,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
not: ¬A,
implies: P ⇒ Q,
false: False,
all: ∀x:A. B[x],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
istype-atom,
eq_atom_wf,
equal-wf-base,
bool_wf,
atom_subtype_base,
assert_wf,
cons_wf,
nat_wf,
istype-void,
istype-le,
nil_wf,
bnot_wf,
not_wf,
istype-assert,
uiff_transitivity,
eqtt_to_assert,
assert_of_eq_atom,
iff_transitivity,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalHypSubstitution,
hypothesis,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
tokenEquality,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
atomEquality,
because_Cache,
productEquality,
independent_pairEquality,
dependent_set_memberEquality_alt,
natural_numberEquality,
independent_pairFormation,
lambdaFormation_alt,
voidElimination,
equalityIstype,
inhabitedIsType,
sqequalBase,
equalitySymmetry,
functionIsType,
unionElimination,
equalityElimination,
independent_functionElimination,
productElimination,
independent_isectElimination,
equalityTransitivity,
dependent_functionElimination
Latex:
\mforall{}[t:Atom]. (ctt-opid-arity(t) \mmember{} (\mBbbN{} \mtimes{} \mBbbN{}) List)
Date html generated:
2020_05_20-PM-08_18_48
Last ObjectModification:
2020_02_25-PM-01_42_48
Theory : cubical!type!theory
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