Nuprl Lemma : s-hd_wf
∀[A:Type]. ∀[s:stream(A)]. (s-hd(s) ∈ A)
Proof
Definitions occuring in Statement :
s-hd: s-hd(s),
stream: stream(A),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
s-hd: s-hd(s),
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
stream-ext,
subtype_rel_weakening,
stream_wf,
pi1_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
cumulativity,
productEquality,
independent_isectElimination,
lambdaFormation,
lambdaEquality,
productElimination,
independent_pairEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[s:stream(A)]. (s-hd(s) \mmember{} A)
Date html generated:
2017_04_14-AM-07_47_03
Last ObjectModification:
2017_02_27-PM-03_16_59
Theory : co-recursion
Home
Index