Nuprl Lemma : correct-sort-arity_wf
∀[opr:Type]. ∀[sort:term(opr) ⟶ ℕ]. ∀[arity:opr ⟶ ((ℕ × ℕ) List)]. ∀[t:term(opr)].
(correct-sort-arity(sort;arity;t) ∈ ℙ)
Proof
Definitions occuring in Statement :
correct-sort-arity: correct-sort-arity(sort;arity;t),
term: term(opr),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
correct-sort-arity: correct-sort-arity(sort;arity;t),
let: let,
implies: P ⇒ Q,
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat: ℕ,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x]
Lemmas referenced :
not_wf,
assert_wf,
isvarterm_wf,
equal-wf-base,
all_wf,
int_seg_wf,
set_subtype_base,
le_wf,
int_subtype_base,
length_wf,
bound-term_wf,
term-bts_wf,
term_wf,
list_wf,
nat_wf,
istype-nat,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productEquality,
because_Cache,
closedConclusion,
natural_numberEquality,
equalityTransitivity,
equalitySymmetry,
lambdaEquality_alt,
applyEquality,
setElimination,
rename,
productElimination,
inhabitedIsType,
independent_isectElimination,
universeIsType,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
functionIsType,
instantiate,
universeEquality
Latex:
\mforall{}[opr:Type]. \mforall{}[sort:term(opr) {}\mrightarrow{} \mBbbN{}]. \mforall{}[arity:opr {}\mrightarrow{} ((\mBbbN{} \mtimes{} \mBbbN{}) List)]. \mforall{}[t:term(opr)].
(correct-sort-arity(sort;arity;t) \mmember{} \mBbbP{})
Date html generated:
2020_05_19-PM-09_58_10
Last ObjectModification:
2020_03_11-PM-03_54_25
Theory : terms
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