Nuprl Lemma : hd-stream-zip
∀[f:Top]. ∀[as,bs:stream(Top)]. (s-hd(stream-zip(f;as;bs)) ~ f s-hd(as) s-hd(bs))
Proof
Definitions occuring in Statement :
stream-zip: stream-zip(f;as;bs),
s-hd: s-hd(s),
stream: stream(A),
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
s-nth: s-nth(n;s),
eq_int: (i =z j),
subtract: n - m,
ifthenelse: if b then t else f fi ,
btrue: tt,
pi1: fst(t),
s-hd: s-hd(s)
Lemmas referenced :
nth-stream-zip,
false_wf,
le_wf,
stream_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
lambdaFormation,
hypothesis,
callbyvalueReduce,
sqleReflexivity,
sqequalAxiom,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[f:Top]. \mforall{}[as,bs:stream(Top)]. (s-hd(stream-zip(f;as;bs)) \msim{} f s-hd(as) s-hd(bs))
Date html generated:
2016_05_14-AM-06_23_35
Last ObjectModification:
2015_12_26-AM-11_58_46
Theory : co-recursion
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