Nuprl Lemma : length-zip-map
∀[L:Top List]. ∀[f,g:Top]. (||zip(map(f;L);map(g;L))|| ~ ||L||)
Proof
Definitions occuring in Statement :
zip: zip(as;bs),
length: ||as||,
map: map(f;as),
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top
Lemmas referenced :
top_wf,
list_wf,
zip-map,
length-map
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
sqequalAxiom,
lemma_by_obid,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
voidElimination,
voidEquality
Latex:
\mforall{}[L:Top List]. \mforall{}[f,g:Top]. (||zip(map(f;L);map(g;L))|| \msim{} ||L||)
Date html generated:
2016_05_15-PM-03_58_45
Last ObjectModification:
2015_12_27-PM-03_06_23
Theory : general
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