Nuprl Lemma : wfterm-hered-correct-sort-arity
∀[opr:Type]. ∀[sort:term(opr) ⟶ ℕ]. ∀[arity:opr ⟶ ((ℕ × ℕ) List)].
wfterm(opr;sort;arity) ≡ hered-term(opr;t.correct-sort-arity(sort;arity;t))
Proof
Definitions occuring in Statement :
wfterm: wfterm(opr;sort;arity),
correct-sort-arity: correct-sort-arity(sort;arity;t),
hered-term: hered-term(opr;t.P[t]),
term: term(opr),
list: T List,
nat: ℕ,
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
wfterm: wfterm(opr;sort;arity),
hered-term: hered-term(opr;t.P[t]),
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
prop: ℙ
Lemmas referenced :
wf-term-hereditarily-correct-sort-arity,
subtype_rel_sets_simple,
term_wf,
assert_wf,
wf-term_wf,
hereditarily_wf,
correct-sort-arity_wf,
istype-assert,
wfterm_wf,
hered-term_wf,
istype-universe
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
independent_pairFormation,
lambdaEquality_alt,
applyEquality,
sqequalRule,
universeIsType,
inhabitedIsType,
because_Cache,
independent_isectElimination,
lambdaFormation_alt,
productElimination,
independent_functionElimination,
independent_pairEquality,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
instantiate,
universeEquality
Latex:
\mforall{}[opr:Type]. \mforall{}[sort:term(opr) {}\mrightarrow{} \mBbbN{}]. \mforall{}[arity:opr {}\mrightarrow{} ((\mBbbN{} \mtimes{} \mBbbN{}) List)].
wfterm(opr;sort;arity) \mequiv{} hered-term(opr;t.correct-sort-arity(sort;arity;t))
Date html generated:
2020_05_19-PM-09_58_28
Last ObjectModification:
2020_03_11-PM-04_30_21
Theory : terms
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