Nuprl Lemma : stream-decomp
∀[s:stream(Top)]. (s ~ s-hd(s).s-tl(s))
Proof
Definitions occuring in Statement :
s-cons: x.s,
s-tl: s-tl(s),
s-hd: s-hd(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,
all: ∀x:A. B[x],
implies: P ⇒ Q,
s-tl: s-tl(s),
s-hd: s-hd(s),
s-cons: x.s,
pi1: fst(t),
pi2: snd(t),
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
top_wf,
stream_wf,
equal_wf,
stream-ext,
subtype_rel_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
productEquality,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
lambdaFormation,
productElimination,
sqequalRule,
equalityTransitivity,
equalitySymmetry,
hypothesisEquality,
dependent_functionElimination,
independent_functionElimination,
sqequalAxiom,
applyEquality,
independent_isectElimination
Latex:
\mforall{}[s:stream(Top)]. (s \msim{} s-hd(s).s-tl(s))
Date html generated:
2017_04_14-AM-07_47_09
Last ObjectModification:
2017_02_27-PM-03_17_06
Theory : co-recursion
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