Nuprl Lemma : ml-accum-abort-sq
∀[A,B:Type]. ∀[F:A ⟶ B ⟶ (B?)].
∀[L:A List]. ∀[s:B?]. (ml-accum-abort(F;s;L) ~ accumulate_abort(x,sofar.F x sofar;s;L))
supposing valueall-type(A) ∧ valueall-type(B) ∧ A ∧ B
Proof
Definitions occuring in Statement :
ml-accum-abort: ml-accum-abort(f;sofar;L),
accumulate_abort: accumulate_abort(x,sofar.F[x; sofar];s;L),
list: T List,
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
unit: Unit,
apply: f a,
function: x:A ⟶ B[x],
union: left + right,
universe: Type,
sqequal: s ~ t
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,
ml-accum-abort: ml-accum-abort(f;sofar;L),
unit: Unit,
so_lambda: λ2x.t[x],
so_apply: x[s],
squash: ↓T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
ifthenelse: if b then t else f fi ,
btrue: tt,
cons: [a / b],
colength: colength(L),
decidable: Dec(P),
nil: [],
it: ⋅,
sq_type: SQType(T),
less_than: a < b,
less_than': less_than'(a;b),
bor: p ∨bq,
bfalse: ff,
spreadcons: spreadcons,
isr: isr(x),
outl: outl(x),
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a)
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,
unit_wf2,
equal-wf-T-base,
nat_wf,
colength_wf_list,
less_than_transitivity1,
less_than_irreflexivity,
list-cases,
ml_apply-sq,
list_wf,
nil_wf,
list-valueall-type,
void-valueall-type,
union-valueall-type,
equal-valueall-type,
function-valueall-type,
function-value-type,
union-value-type,
accumulate_abort_nil_lemma,
null_nil_lemma,
testxxx_lemma,
product_subtype_list,
spread_cons_lemma,
intformeq_wf,
itermAdd_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
le_wf,
equal_wf,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
decidable__equal_int,
cons_wf,
accumulate_abort_cons_lemma,
null_cons_lemma,
valueall-type_wf,
valueall-type-has-valueall,
evalall-reduce,
ml_apply_wf,
accumulate_abort-aborted,
subtype_rel_list,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
independent_functionElimination,
sqequalAxiom,
unionEquality,
cumulativity,
productElimination,
applyEquality,
because_Cache,
unionElimination,
functionEquality,
imageMemberEquality,
baseClosed,
promote_hyp,
hypothesis_subsumption,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
dependent_set_memberEquality,
addEquality,
instantiate,
imageElimination,
productEquality,
universeEquality,
functionExtensionality,
callbyvalueReduce,
inrEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[F:A {}\mrightarrow{} B {}\mrightarrow{} (B?)].
\mforall{}[L:A List]. \mforall{}[s:B?]. (ml-accum-abort(F;s;L) \msim{} accumulate\_abort(x,sofar.F x sofar;s;L))
supposing valueall-type(A) \mwedge{} valueall-type(B) \mwedge{} A \mwedge{} B
Date html generated:
2017_09_29-PM-05_57_12
Last ObjectModification:
2017_05_21-PM-04_48_42
Theory : omega
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