Nuprl Lemma : index-split_wf
∀[T:Type]. ∀[L:T List]. ∀[ids:ℕ List]. (index-split(L;ids) ∈ T List × (T List))
Proof
Definitions occuring in Statement :
index-split: index-split(L;idxs),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
index-split: index-split(L;idxs),
let: let,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
uimplies: b supposing a,
int_seg: {i..j-},
prop: ℙ,
nat: ℕ
Lemmas referenced :
firstn_wf,
permute-to-front_wf,
length_wf,
filter_wf5,
upto_wf,
l_member_wf,
subtype_rel_list,
int_seg_wf,
int-list-member_wf,
nat_wf,
nth_tl_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
independent_pairEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
because_Cache,
hypothesis,
intEquality,
applyEquality,
lambdaEquality,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
setElimination,
rename,
dependent_functionElimination,
setEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[ids:\mBbbN{} List]. (index-split(L;ids) \mmember{} T List \mtimes{} (T List))
Date html generated:
2016_05_15-PM-04_24_34
Last ObjectModification:
2015_12_27-PM-02_52_26
Theory : general
Home
Index