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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