Nuprl Lemma : s-cons_wf
∀[A:Type]. ∀[x:A]. ∀[s:stream(A)]. (x.s ∈ stream(A))
Proof
Definitions occuring in Statement :
s-cons: x.s,
stream: stream(A),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
s-cons: x.s,
subtype_rel: A ⊆r B,
ext-eq: A ≡ B,
and: P ∧ Q
Lemmas referenced :
stream_wf,
stream-ext
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
independent_pairEquality,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalHypSubstitution,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
isect_memberEquality,
because_Cache,
universeEquality,
productElimination
Latex:
\mforall{}[A:Type]. \mforall{}[x:A]. \mforall{}[s:stream(A)]. (x.s \mmember{} stream(A))
Date html generated:
2016_05_14-AM-06_22_27
Last ObjectModification:
2015_12_26-AM-11_59_26
Theory : co-recursion
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