Nuprl Lemma : iterate-fun-stream_wf
∀[A:Type]. ∀[x:A]. ∀[f:A ⟶ A]. (iterate-fun-stream(f;x) ∈ stream(A))
Proof
Definitions occuring in Statement :
iterate-fun-stream: iterate-fun-stream(f;x),
stream: stream(A),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iterate-fun-stream: iterate-fun-stream(f;x),
stream: stream(A),
so_lambda: λ2x.t[x],
so_apply: x[s],
isect2: T1 ⋂ T2,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
top: Top,
bfalse: ff,
s-cons: x.s
Lemmas referenced :
fix_wf_corec_parameter,
top_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
productEquality,
hypothesisEquality,
universeEquality,
because_Cache,
isect_memberEquality,
unionElimination,
equalityElimination,
functionExtensionality,
voidElimination,
voidEquality,
hypothesis,
independent_pairEquality,
applyEquality,
cumulativity,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[A:Type]. \mforall{}[x:A]. \mforall{}[f:A {}\mrightarrow{} A]. (iterate-fun-stream(f;x) \mmember{} stream(A))
Date html generated:
2016_05_14-AM-06_24_48
Last ObjectModification:
2015_12_26-AM-11_58_25
Theory : co-recursion
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