Nuprl Lemma : map-iterate-fun-stream
∀[f,x:Top]. (iterate-fun-stream(f;f x) ~ stream-map(f;iterate-fun-stream(f;x)))
Proof
Definitions occuring in Statement :
iterate-fun-stream: iterate-fun-stream(f;x),
stream-map: stream-map(f;s),
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iterate-fun-stream: iterate-fun-stream(f;x),
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
all: ∀x:A. B[x],
top: Top,
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
not: ¬A,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
subtract: n - m,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
nat_plus: ℕ+,
stream-map: stream-map(f;s),
s-cons: x.s
Lemmas referenced :
top_wf,
is-exception_wf,
int_subtype_base,
has-value_wf_base,
fun_exp_unroll_1,
le-add-cancel,
add-zero,
add_functionality_wrt_le,
add-commutes,
add-swap,
add-associates,
minus-minus,
minus-add,
minus-one-mul-top,
zero-add,
minus-one-mul,
condition-implies-le,
less-iff-le,
not-ge-2,
false_wf,
subtract_wf,
decidable__le,
bottom-sqle,
strictness-apply,
fun_exp0_lemma,
base_wf,
less_than_wf,
ge_wf,
less_than_irreflexivity,
less_than_transitivity1,
nat_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalSqle,
sqleRule,
thin,
fixpointLeast,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
independent_functionElimination,
voidElimination,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
axiomSqleEquality,
isect_memberEquality,
voidEquality,
unionElimination,
independent_pairFormation,
productElimination,
addEquality,
applyEquality,
intEquality,
minusEquality,
because_Cache,
divergentSqle,
dependent_set_memberEquality,
baseApply,
closedConclusion,
baseClosed,
sqleReflexivity,
sqequalAxiom
Latex:
\mforall{}[f,x:Top]. (iterate-fun-stream(f;f x) \msim{} stream-map(f;iterate-fun-stream(f;x)))
Date html generated:
2016_05_14-AM-06_24_53
Last ObjectModification:
2016_01_14-PM-08_02_54
Theory : co-recursion
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