Nuprl Lemma : tl-stream-zip
∀[f:Top]. ∀[as,bs:stream(Top)]. (s-tl(stream-zip(f;as;bs)) ~ stream-zip(f;s-tl(as);s-tl(bs)))
Proof
Definitions occuring in Statement :
stream-zip: stream-zip(f;as;bs),
s-tl: s-tl(s),
stream: stream(A),
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
stream-zip: stream-zip(f;as;bs),
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
s-tl: s-tl(s),
pi2: snd(t),
prop: ℙ
Lemmas referenced :
stream_wf,
top_wf,
stream-ext,
subtype_rel_weakening,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesis,
sqequalAxiom,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
hypothesisEquality,
because_Cache,
applyEquality,
productEquality,
independent_isectElimination,
lambdaFormation,
productElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[f:Top]. \mforall{}[as,bs:stream(Top)]. (s-tl(stream-zip(f;as;bs)) \msim{} stream-zip(f;s-tl(as);s-tl(bs)))
Date html generated:
2017_04_14-AM-07_47_48
Last ObjectModification:
2017_02_27-PM-03_18_15
Theory : co-recursion
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