Nuprl Lemma : is_list_splitting_wf
∀[T:Type]. ∀[L:T List]. ∀[LL:T List List]. ∀[L2:T List]. ∀[f:(T List) ⟶ 𝔹]. (is_list_splitting(T;L;LL;L2;f) ∈ ℙ)
Proof
Definitions occuring in Statement :
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
list: T List,
bool: 𝔹,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
prop: ℙ,
and: P ∧ Q,
top: Top,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
implies: P ⇒ Q,
so_apply: x[s]
Lemmas referenced :
equal_wf,
list_wf,
append_wf,
concat_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,
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,
applyLambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaEquality,
lambdaFormation,
setElimination,
rename,
applyEquality,
independent_isectElimination,
functionEquality,
setEquality,
functionExtensionality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[LL:T List List]. \mforall{}[L2:T List]. \mforall{}[f:(T List) {}\mrightarrow{} \mBbbB{}].
(is\_list\_splitting(T;L;LL;L2;f) \mmember{} \mBbbP{})
Date html generated:
2018_05_21-PM-08_04_30
Last ObjectModification:
2017_07_26-PM-05_40_35
Theory : general
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