Nuprl Lemma : mk-stream_wf
∀[A:Type]. ∀[f:A ⟶ A]. ∀[x:A]. mk-stream(f;x) ∈ stream(A) supposing valueall-type(A)
Proof
Definitions occuring in Statement :
mk-stream: mk-stream(f;x),
stream: stream(A),
valueall-type: valueall-type(T),
uimplies: b supposing 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,
uimplies: b supposing a,
mk-stream: mk-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,
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a)
Lemmas referenced :
fix_wf_corec_parameter,
top_wf,
valueall-type-has-valueall,
evalall-reduce,
bool_wf,
valueall-type_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,
independent_isectElimination,
applyEquality,
callbyvalueReduce,
cumulativity,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[A:Type]. \mforall{}[f:A {}\mrightarrow{} A]. \mforall{}[x:A]. mk-stream(f;x) \mmember{} stream(A) supposing valueall-type(A)
Date html generated:
2016_05_14-AM-06_23_03
Last ObjectModification:
2015_12_26-AM-11_59_06
Theory : co-recursion
Home
Index