Nuprl Lemma : mkwfterm_wf
∀[opr:Type]. ∀[sort:term(opr) ⟶ ℕ]. ∀[arity:opr ⟶ ((ℕ × ℕ) List)]. ∀[f:opr]. ∀[bts:wf-bound-terms(opr;sort;arity;f)].
  (mkwfterm(f;bts) ∈ wfterm(opr;sort;arity))
Proof
Definitions occuring in Statement : 
mkwfterm: mkwfterm(f;bts)
, 
wf-bound-terms: wf-bound-terms(opr;sort;arity;f)
, 
wfterm: wfterm(opr;sort;arity)
, 
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 : 
mkwfterm: mkwfterm(f;bts)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
wf-bound-terms: wf-bound-terms(opr;sort;arity;f)
, 
wfterm: wfterm(opr;sort;arity)
, 
subtype_rel: A ⊆r B
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
all: ∀x:A. B[x]
, 
uiff: uiff(P;Q)
, 
cand: A c∧ B
, 
guard: {T}
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
le: A ≤ B
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
prop: ℙ
, 
pi2: snd(t)
, 
sq_stable: SqStable(P)
, 
squash: ↓T
Lemmas referenced : 
mkterm_wf, 
subtype_rel_list, 
list_wf, 
varname_wf, 
wfterm_wf, 
term_wf, 
subtype_rel_product, 
assert-wf-mkterm, 
int_seg_wf, 
length_wf, 
istype-assert, 
wf-term_wf, 
wf-bound-terms_wf, 
nat_wf, 
istype-nat, 
istype-universe, 
select_wf, 
int_seg_properties, 
decidable__le, 
full-omega-unsat, 
intformand_wf, 
intformnot_wf, 
intformle_wf, 
itermConstant_wf, 
itermVar_wf, 
istype-int, 
int_formula_prop_and_lemma, 
int_formula_prop_not_lemma, 
int_formula_prop_le_lemma, 
int_term_value_constant_lemma, 
int_term_value_var_lemma, 
int_formula_prop_wf, 
decidable__lt, 
intformless_wf, 
int_formula_prop_less_lemma, 
sq_stable_from_decidable, 
assert_wf, 
decidable__assert
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation_alt, 
introduction, 
cut, 
sqequalHypSubstitution, 
setElimination, 
thin, 
rename, 
dependent_set_memberEquality_alt, 
extract_by_obid, 
isectElimination, 
hypothesisEquality, 
applyEquality, 
productElimination, 
productEquality, 
hypothesis, 
independent_isectElimination, 
lambdaEquality_alt, 
universeIsType, 
because_Cache, 
lambdaFormation_alt, 
dependent_functionElimination, 
independent_pairFormation, 
natural_numberEquality, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
isect_memberEquality_alt, 
isectIsTypeImplies, 
inhabitedIsType, 
functionIsType, 
instantiate, 
universeEquality, 
unionElimination, 
approximateComputation, 
independent_functionElimination, 
dependent_pairFormation_alt, 
int_eqEquality, 
Error :memTop, 
voidElimination, 
imageMemberEquality, 
baseClosed, 
imageElimination, 
equalityIstype
Latex:
\mforall{}[opr:Type].  \mforall{}[sort:term(opr)  {}\mrightarrow{}  \mBbbN{}].  \mforall{}[arity:opr  {}\mrightarrow{}  ((\mBbbN{}  \mtimes{}  \mBbbN{})  List)].  \mforall{}[f:opr].
\mforall{}[bts:wf-bound-terms(opr;sort;arity;f)].
    (mkwfterm(f;bts)  \mmember{}  wfterm(opr;sort;arity))
Date html generated:
2020_05_19-PM-09_58_36
Last ObjectModification:
2020_03_09-PM-04_10_23
Theory : terms
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