Nuprl Lemma : wfbts_wf
∀[opr:Type]. ∀[sort:term(opr) ⟶ ℕ]. ∀[arity:opr ⟶ ((ℕ × ℕ) List)]. ∀[t:wfterm(opr;sort;arity)].
wfbts(t) ∈ wf-bound-terms(opr;sort;arity;term-opr(t)) supposing ¬↑isvarterm(t)
Proof
Definitions occuring in Statement :
wfbts: wfbts(t),
wf-bound-terms: wf-bound-terms(opr;sort;arity;f),
wfterm: wfterm(opr;sort;arity),
term-opr: term-opr(t),
isvarterm: isvarterm(t),
term: term(opr),
list: T List,
nat: ℕ,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
wfterm: wfterm(opr;sort;arity),
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
bound-term: bound-term(opr),
uiff: uiff(P;Q),
wf-bound-terms: wf-bound-terms(opr;sort;arity;f),
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
pi1: fst(t),
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
pi2: snd(t),
not: ¬A,
false: False,
prop: ℙ,
wfbts: wfbts(t),
squash: ↓T,
true: True,
guard: {T},
rev_implies: P ⇐ Q,
mkterm: mkterm(opr;bts),
term-bts: term-bts(t),
outr: outr(x),
cand: A c∧ B,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
ge: i ≥ j ,
sq_type: SQType(T),
cons: [a / b],
less_than': less_than'(a;b),
colength: colength(L),
nil: [],
it: ⋅,
less_than: a < b,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
select: L[n],
nat_plus: ℕ+,
subtract: n - m,
term-opr: term-opr(t)
Lemmas referenced :
assert-not-isvarterm,
assert-wf-mkterm,
istype-int,
length_wf_nat,
list_wf,
varname_wf,
wfterm_wf,
set_subtype_base,
le_wf,
int_subtype_base,
nat_wf,
term-opr_wf,
int_seg_wf,
length_wf,
istype-assert,
isvarterm_wf,
istype-void,
term_wf,
istype-nat,
istype-universe,
wf-term_wf,
assert_wf,
equal_wf,
squash_wf,
true_wf,
bound-term_wf,
term-bts_wf,
not_wf,
subtype_rel_self,
iff_weakening_equal,
select_wf,
less_than_wf,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
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,
subtype_base_sq,
non_neg_length,
istype-le,
nat_properties,
ge_wf,
istype-less_than,
list-cases,
product_subtype_list,
colength-cons-not-zero,
colength_wf_list,
subtract-1-ge-0,
intformeq_wf,
int_formula_prop_eq_lemma,
spread_cons_lemma,
decidable__equal_int,
subtract_wf,
itermSubtract_wf,
itermAdd_wf,
int_term_value_subtract_lemma,
int_term_value_add_lemma,
length_of_nil_lemma,
stuck-spread,
istype-base,
nil_wf,
cons_wf,
length_of_cons_lemma,
add-is-int-iff,
false_wf,
istype-false,
add_nat_plus,
nat_plus_properties,
add-member-int_seg2,
select_cons_tl_sq2,
int_seg_subtype_nat,
pi1_wf,
subtype_rel_list,
subtype_rel_product,
pi2_wf,
equal-wf-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
setElimination,
rename,
because_Cache,
productElimination,
independent_functionElimination,
sqequalRule,
independent_isectElimination,
dependent_set_memberEquality_alt,
productIsType,
equalityIstype,
productEquality,
applyEquality,
intEquality,
lambdaEquality_alt,
natural_numberEquality,
sqequalBase,
equalitySymmetry,
functionIsType,
universeIsType,
inhabitedIsType,
lambdaFormation_alt,
equalityTransitivity,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
instantiate,
universeEquality,
hyp_replacement,
independent_pairFormation,
applyLambdaEquality,
imageElimination,
imageMemberEquality,
baseClosed,
unionElimination,
approximateComputation,
dependent_pairFormation_alt,
int_eqEquality,
Error :memTop,
voidElimination,
cumulativity,
intWeakElimination,
functionIsTypeImplies,
promote_hyp,
hypothesis_subsumption,
baseApply,
closedConclusion,
independent_pairEquality,
addEquality,
pointwiseFunctionality
Latex:
\mforall{}[opr:Type]. \mforall{}[sort:term(opr) {}\mrightarrow{} \mBbbN{}]. \mforall{}[arity:opr {}\mrightarrow{} ((\mBbbN{} \mtimes{} \mBbbN{}) List)]. \mforall{}[t:wfterm(opr;sort;arity)].
wfbts(t) \mmember{} wf-bound-terms(opr;sort;arity;term-opr(t)) supposing \mneg{}\muparrow{}isvarterm(t)
Date html generated:
2020_05_19-PM-09_58_44
Last ObjectModification:
2020_03_09-PM-04_10_26
Theory : terms
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