Nuprl Lemma : is_accum_splitting_wf
∀[T,A:Type]. ∀[L:T List]. ∀[LL:(T List × A) List]. ∀[L2:T List × A]. ∀[f:(T List × A) ⟶ 𝔹]. ∀[x:A].
∀[g:(T List × A) ⟶ A].
(is_accum_splitting(T;A;L;LL;L2;f;g;x) ∈ ℙ)
Proof
Definitions occuring in Statement :
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
list: T List,
bool: 𝔹,
uall: ∀[x:A]. B[x],
prop: ℙ,
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,
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
prop: ℙ,
and: P ∧ Q,
pi1: fst(t),
top: Top,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
implies: P ⇒ Q,
pi2: snd(t),
so_apply: x[s],
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
less_than: a < b,
squash: ↓T
Lemmas referenced :
equal_wf,
list_wf,
append_wf,
concat_wf,
map_wf,
length_wf,
length-append,
l_all_wf2,
not_wf,
assert_wf,
null_wf3,
subtype_rel_list,
top_wf,
all_wf,
l_member_wf,
iseg_wf,
hd_wf,
cons_wf,
nil_wf,
length_nil,
non_neg_length,
length_cons,
length_append,
pi1_wf_top,
length_of_cons_lemma,
length_of_nil_lemma,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_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_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
pi2_wf,
int_seg_wf,
select_wf,
int_seg_properties,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
because_Cache,
lambdaEquality,
productElimination,
applyLambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaFormation,
setElimination,
rename,
applyEquality,
independent_isectElimination,
functionEquality,
independent_pairEquality,
setEquality,
functionExtensionality,
dependent_functionElimination,
natural_numberEquality,
equalityTransitivity,
equalitySymmetry,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
addEquality,
imageElimination,
axiomEquality,
universeEquality
Latex:
\mforall{}[T,A:Type]. \mforall{}[L:T List]. \mforall{}[LL:(T List \mtimes{} A) List]. \mforall{}[L2:T List \mtimes{} A]. \mforall{}[f:(T List \mtimes{} A) {}\mrightarrow{} \mBbbB{}]. \mforall{}[x:A].
\mforall{}[g:(T List \mtimes{} A) {}\mrightarrow{} A].
(is\_accum\_splitting(T;A;L;LL;L2;f;g;x) \mmember{} \mBbbP{})
Date html generated:
2018_05_21-PM-08_06_01
Last ObjectModification:
2017_07_26-PM-05_42_01
Theory : general
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