Nuprl Lemma : stream-bijection
∀[A:Type]. Bij(stream(A);ℕ ⟶ A;λs,n. s-nth(n;s))
Proof
Definitions occuring in Statement :
s-nth: s-nth(n;s),
stream: stream(A),
biject: Bij(A;B;f),
nat: ℕ,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
biject: Bij(A;B;f),
and: P ∧ Q,
inject: Inj(A;B;f),
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
surject: Surj(A;B;f),
uimplies: b supposing a,
exists: ∃x:A. B[x],
top: Top,
subtype_rel: A ⊆r B
Lemmas referenced :
nat_wf,
s-nth_wf,
stream_wf,
stream-extensionality,
stream-map_wf,
nats_wf,
nth-stream-map,
istype-void,
stream-subtype,
top_wf,
nth-nats
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
Error :universeIsType,
universeEquality,
independent_pairFormation,
Error :lambdaFormation_alt,
sqequalRule,
cut,
hypothesis,
Error :equalityIsType1,
Error :functionIsType,
introduction,
extract_by_obid,
hypothesisEquality,
Error :lambdaEquality_alt,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
because_Cache,
Error :inhabitedIsType,
independent_isectElimination,
applyLambdaEquality,
applyEquality,
Error :dependent_pairFormation_alt,
Error :functionExtensionality_alt,
Error :isect_memberEquality_alt,
voidElimination,
dependent_functionElimination
Latex:
\mforall{}[A:Type]. Bij(stream(A);\mBbbN{} {}\mrightarrow{} A;\mlambda{}s,n. s-nth(n;s))
Date html generated:
2019_06_20-PM-00_37_46
Last ObjectModification:
2018_10_02-AM-10_06_13
Theory : co-recursion
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