Nuprl Lemma : wf-bound-terms_wf
∀[opr:Type]. ∀[sort:term(opr) ⟶ ℕ]. ∀[arity:opr ⟶ ((ℕ × ℕ) List)]. ∀[f:opr].
(wf-bound-terms(opr;sort;arity;f) ∈ Type)
Proof
Definitions occuring in Statement :
wf-bound-terms: wf-bound-terms(opr;sort;arity;f),
term: term(opr),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
pi2: snd(t),
implies: P ⇒ Q,
all: ∀x:A. B[x],
uimplies: b supposing a,
so_apply: x[s],
le: A ≤ B,
lelt: i ≤ j < k,
int_seg: {i..j-},
nat: ℕ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
wf-bound-terms: wf-bound-terms(opr;sort;arity;f),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-universe,
istype-nat,
term_wf,
nat_wf,
length_wf,
int_subtype_base,
le_wf,
set_subtype_base,
int_seg_wf,
all_wf,
equal-wf-base,
wfterm_wf,
varname_wf,
list_wf
Rules used in proof :
universeEquality,
instantiate,
functionIsType,
isectIsTypeImplies,
isect_memberEquality_alt,
axiomEquality,
universeIsType,
independent_functionElimination,
dependent_functionElimination,
equalityIstype,
lambdaFormation_alt,
independent_isectElimination,
inhabitedIsType,
productElimination,
rename,
setElimination,
applyEquality,
lambdaEquality_alt,
equalitySymmetry,
equalityTransitivity,
natural_numberEquality,
closedConclusion,
because_Cache,
hypothesisEquality,
hypothesis,
productEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
setEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[opr:Type]. \mforall{}[sort:term(opr) {}\mrightarrow{} \mBbbN{}]. \mforall{}[arity:opr {}\mrightarrow{} ((\mBbbN{} \mtimes{} \mBbbN{}) List)]. \mforall{}[f:opr].
(wf-bound-terms(opr;sort;arity;f) \mmember{} Type)
Date html generated:
2020_05_19-PM-09_58_32
Last ObjectModification:
2020_03_11-PM-04_17_16
Theory : terms
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