Nuprl Lemma : accumulate_abort_wf
∀[A,B:Type]. ∀[s:B?]. ∀[F:A ⟶ B ⟶ (B?)]. ∀[L:A List].
accumulate_abort(x,sofar.F[x;sofar];s;L) ∈ B? supposing valueall-type(B)
Proof
Definitions occuring in Statement :
accumulate_abort: accumulate_abort(x,sofar.F[x; sofar];s;L),
list: T List,
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
unit: Unit,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
accumulate_abort: accumulate_abort(x,sofar.F[x; sofar];s;L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q,
unit: Unit
Lemmas referenced :
eager-accum_wf,
unit_wf2,
union-valueall-type,
equal-valueall-type,
valueall-type_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
unionEquality,
hypothesis,
lambdaEquality,
unionElimination,
applyEquality,
inrEquality,
because_Cache,
independent_isectElimination,
independent_functionElimination,
intEquality,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[s:B?]. \mforall{}[F:A {}\mrightarrow{} B {}\mrightarrow{} (B?)]. \mforall{}[L:A List].
accumulate\_abort(x,sofar.F[x;sofar];s;L) \mmember{} B? supposing valueall-type(B)
Date html generated:
2016_05_14-AM-06_55_57
Last ObjectModification:
2015_12_26-PM-01_15_09
Theory : omega
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