Nuprl Lemma : ml-accum-abort_wf
∀[A,B:Type]. ∀[s:B?]. ∀[F:A ⟶ B ⟶ (B?)]. ∀[L:A List].
ml-accum-abort(F;s;L) ∈ B? supposing valueall-type(A) ∧ valueall-type(B) ∧ A ∧ B
Proof
Definitions occuring in Statement :
ml-accum-abort: ml-accum-abort(f;sofar;L),
list: T List,
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
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,
and: P ∧ Q,
cand: A c∧ B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
prop: ℙ
Lemmas referenced :
ml-accum-abort-sq,
accumulate_abort_wf,
valueall-type_wf,
list_wf,
unit_wf2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
extract_by_obid,
isectElimination,
hypothesisEquality,
independent_isectElimination,
hypothesis,
independent_pairFormation,
cumulativity,
lambdaEquality,
applyEquality,
functionExtensionality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
productEquality,
isect_memberEquality,
because_Cache,
functionEquality,
unionEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[s:B?]. \mforall{}[F:A {}\mrightarrow{} B {}\mrightarrow{} (B?)]. \mforall{}[L:A List].
ml-accum-abort(F;s;L) \mmember{} B? supposing valueall-type(A) \mwedge{} valueall-type(B) \mwedge{} A \mwedge{} B
Date html generated:
2017_09_29-PM-05_57_16
Last ObjectModification:
2017_05_21-PM-04_50_07
Theory : omega
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