Nuprl Lemma : list_accum2_wf
∀[A,B,T:Type].
∀[f:T ⟶ A ⟶ B ⟶ T]. ∀[g:T ⟶ A ⟶ T]. ∀[h:T ⟶ B ⟶ T]. ∀[as:A List]. ∀[bs:B List]. ∀[y:T].
(list_accum2(x,a,b.f[x;a;b];x,a.g[x;a];x,b.h[x;b];y;as;bs) ∈ T)
supposing value-type(T)
Proof
Definitions occuring in Statement :
list_accum2: list_accum2(x,a,b.f[x; a; b];x,a.g[x; a];x,b.h[x; b];y;as;bs),
list: T List,
value-type: value-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2;s3],
so_apply: x[s1;s2],
member: t ∈ T,
function: 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],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
or: P ∨ Q,
list_accum2: list_accum2(x,a,b.f[x; a; b];x,a.g[x; a];x,b.h[x; b];y;as;bs),
nil: [],
it: ⋅,
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
has-value: (a)↓,
decidable: Dec(P),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
so_apply: x[s1;s2;s3]
Lemmas referenced :
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
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,
less_than_wf,
list_wf,
equal-wf-T-base,
nat_wf,
colength_wf_list,
less_than_transitivity1,
less_than_irreflexivity,
list-cases,
product_subtype_list,
spread_cons_lemma,
equal_wf,
subtype_base_sq,
set_subtype_base,
le_wf,
int_subtype_base,
value-type-has-value,
intformeq_wf,
itermAdd_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
decidable__equal_int,
nil_wf,
value-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
applyEquality,
because_Cache,
unionElimination,
promote_hyp,
hypothesis_subsumption,
productElimination,
baseClosed,
instantiate,
callbyvalueReduce,
functionExtensionality,
applyLambdaEquality,
dependent_set_memberEquality,
addEquality,
imageElimination,
functionEquality,
universeEquality
Latex:
\mforall{}[A,B,T:Type].
\mforall{}[f:T {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} T]. \mforall{}[g:T {}\mrightarrow{} A {}\mrightarrow{} T]. \mforall{}[h:T {}\mrightarrow{} B {}\mrightarrow{} T]. \mforall{}[as:A List]. \mforall{}[bs:B List]. \mforall{}[y:T].
(list\_accum2(x,a,b.f[x;a;b];x,a.g[x;a];x,b.h[x;b];y;as;bs) \mmember{} T)
supposing value-type(T)
Date html generated:
2017_09_29-PM-05_58_39
Last ObjectModification:
2017_04_24-PM-04_46_41
Theory : list_1
Home
Index