Nuprl Lemma : stream-lex_wf
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. (stream-lex(T;R) ∈ stream(T) ⟶ stream(T) ⟶ ℙ)
Proof
Definitions occuring in Statement :
stream-lex: stream-lex(T;R),
stream: stream(A),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
stream-lex: stream-lex(T;R),
so_lambda: λ2x.t[x],
infix_ap: x f y,
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
bigrel_wf,
stream_wf,
and_wf,
s-hd_wf,
equal_wf,
s-tl_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
functionEquality,
cumulativity,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (stream-lex(T;R) \mmember{} stream(T) {}\mrightarrow{} stream(T) {}\mrightarrow{} \mBbbP{})
Date html generated:
2016_05_14-AM-06_23_57
Last ObjectModification:
2015_12_26-AM-11_58_41
Theory : co-recursion
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