Nuprl Lemma : select-map-index
∀[f:Top]. ∀[L:Top List]. ∀[i:ℕ||L||]. (map-index(f;L)[i] ~ f i L[i])
Proof
Definitions occuring in Statement :
map-index: map-index(f;L),
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
map-index: map-index(f;L),
uall: ∀[x:A]. B[x],
member: t ∈ T,
int_seg: {i..j-}
Lemmas referenced :
select-map-index_aux,
zero-add,
int_seg_wf,
length_wf,
top_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
natural_numberEquality,
hypothesis,
setElimination,
rename,
sqequalAxiom,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[f:Top]. \mforall{}[L:Top List]. \mforall{}[i:\mBbbN{}||L||]. (map-index(f;L)[i] \msim{} f i L[i])
Date html generated:
2016_05_14-PM-03_13_13
Last ObjectModification:
2015_12_26-PM-01_46_27
Theory : list_1
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