Nuprl Lemma : stream-map_wf
∀[A,B:Type]. ∀[f:A ⟶ B]. ∀[s:stream(A)]. (stream-map(f;s) ∈ stream(B))
Proof
Definitions occuring in Statement :
stream-map: stream-map(f;s),
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,
stream-map: stream-map(f;s),
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,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
stream_wf,
fix_wf_corec_parameter,
top_wf,
stream-ext,
subtype_rel_weakening,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
isect_memberEquality,
because_Cache,
functionEquality,
universeEquality,
lambdaEquality,
productEquality,
unionElimination,
equalityElimination,
functionExtensionality,
voidElimination,
voidEquality,
applyEquality,
independent_isectElimination,
lambdaFormation,
spreadEquality,
productElimination,
independent_pairEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[s:stream(A)]. (stream-map(f;s) \mmember{} stream(B))
Date html generated:
2017_04_14-AM-07_47_30
Last ObjectModification:
2017_02_27-PM-03_17_30
Theory : co-recursion
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