Nuprl Lemma : zip_cons_cons_lemma
∀d,c,b,a:Top. (zip([a / b];[c / d]) ~ [<a, c> / zip(b;d)])
Proof
Definitions occuring in Statement :
zip: zip(as;bs),
cons: [a / b],
top: Top,
all: ∀x:A. B[x],
pair: <a, b>,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
zip: zip(as;bs),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3]
Lemmas referenced :
top_wf,
list_ind_cons_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalRule,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}d,c,b,a:Top. (zip([a / b];[c / d]) \msim{} [<a, c> / zip(b;d)])
Date html generated:
2016_05_14-PM-03_14_42
Last ObjectModification:
2015_12_26-PM-01_45_46
Theory : list_1
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