Nuprl Lemma : wf-term_wf
∀[opr:Type]. ∀[sort:term(opr) ⟶ ℕ]. ∀[arity:opr ⟶ ((ℕ × ℕ) List)]. ∀[t:term(opr)]. (wf-term(arity;sort;t) ∈ 𝔹)
Proof
Definitions occuring in Statement :
wf-term: wf-term(arity;sort;t),
term: term(opr),
list: T List,
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
and: P ∧ Q,
prop: ℙ,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
coterm-fun: coterm-fun(opr;T),
wf-term: wf-term(arity;sort;t),
has-value: (a)↓,
uiff: uiff(P;Q),
pi1: fst(t),
pi2: snd(t),
mkterm: mkterm(opr;bts),
bfalse: ff,
band: p ∧b q,
ifthenelse: if b then t else f fi
Lemmas referenced :
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
istype-less_than,
int_seg_properties,
int_seg_wf,
subtract-1-ge-0,
decidable__equal_int,
subtract_wf,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
intformnot_wf,
intformeq_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_subtract_lemma,
decidable__le,
decidable__lt,
istype-le,
subtype_rel_self,
term-ext,
subtype_rel_weakening,
term_wf,
coterm-fun_wf,
ext-eq_inversion,
btrue_wf,
term-size_wf,
value-type-has-value,
list_wf,
nat_wf,
list-value-type,
eq_int_wf,
length_wf,
varname_wf,
bool_cases,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
band_wf,
assert_of_eq_int,
bl-all_wf,
zip_wf,
l_member_wf,
pi1_wf,
subtype_rel_product,
istype-nat,
pi2_wf,
term-size-positive,
bfalse_wf,
itermAdd_wf,
int_term_value_add_lemma,
istype-universe,
term_size_mkterm_lemma,
summand-le-lsum,
member-zip
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
lambdaFormation_alt,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
dependent_functionElimination,
Error :memTop,
independent_pairFormation,
universeIsType,
voidElimination,
isect_memberEquality_alt,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsTypeImplies,
inhabitedIsType,
isectIsTypeImplies,
productElimination,
unionElimination,
applyEquality,
instantiate,
because_Cache,
applyLambdaEquality,
dependent_set_memberEquality_alt,
productIsType,
promote_hyp,
hypothesis_subsumption,
callbyvalueReduce,
productEquality,
closedConclusion,
cumulativity,
intEquality,
setIsType,
equalityIstype,
addEquality,
functionIsType,
universeEquality,
independent_pairEquality
Latex:
\mforall{}[opr:Type]. \mforall{}[sort:term(opr) {}\mrightarrow{} \mBbbN{}]. \mforall{}[arity:opr {}\mrightarrow{} ((\mBbbN{} \mtimes{} \mBbbN{}) List)]. \mforall{}[t:term(opr)].
(wf-term(arity;sort;t) \mmember{} \mBbbB{})
Date html generated:
2020_05_19-PM-09_58_15
Last ObjectModification:
2020_03_12-AM-10_44_21
Theory : terms
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