Nuprl Lemma : stream-ext
∀[A:Type]. stream(A) ≡ A × stream(A)
Proof
Definitions occuring in Statement :
stream: stream(A),
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
stream: stream(A),
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
corec-ext,
continuous-monotone-product,
continuous-monotone-constant,
continuous-monotone-id
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
productEquality,
hypothesisEquality,
universeEquality,
independent_isectElimination,
hypothesis,
productElimination,
independent_pairEquality,
axiomEquality
Latex:
\mforall{}[A:Type]. stream(A) \mequiv{} A \mtimes{} stream(A)
Date html generated:
2016_05_14-AM-06_22_07
Last ObjectModification:
2015_12_26-AM-11_59_39
Theory : co-recursion
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