Nuprl Lemma : es-class-reply-or-fail_wf
∀[Info,A,B:Type]. ∀[loc1:A ─→ Id]. ∀[loc2:B ─→ Id]. ∀[es:EO+(Info)]. ∀[f:Id List]. ∀[X:EClass(A)]. ∀[Y:EClass(B)].
∀[R:E(X) ─→ A ─→ B ─→ ℙ].
(∀e,x,y. e∈X(x) ⇐c⇒ ∃ reply Y(y)@loc1[x] such that
R[e;x;y]∧loc2[y]=loc(e)
unless loc(e) ∈ f ∈ ℙ)
Proof
Definitions occuring in Statement :
es-class-reply-or-fail: es-class-reply-or-fail,
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2;s3],
so_apply: x[s],
member: t ∈ T,
function: x:A ─→ B[x],
universe: Type
Lemmas :
all_wf,
es-E-interface_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
top_wf,
exists_wf,
es-causle_wf,
es-loc_wf,
eclass-val_wf,
assert_elim,
in-eclass_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
or_wf,
l_member_wf,
event-ordering+_wf,
eclass_wf,
list_wf,
Id_wf
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[loc1:A {}\mrightarrow{} Id]. \mforall{}[loc2:B {}\mrightarrow{} Id]. \mforall{}[es:EO+(Info)]. \mforall{}[f:Id List]. \mforall{}[X:EClass(A)].
\mforall{}[Y:EClass(B)]. \mforall{}[R:E(X) {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} \mBbbP{}].
(\mforall{}e,x,y. e\mmember{}X(x) \mLeftarrow{}c\mRightarrow{} \mexists{} reply Y(y)@loc1[x] such that
R[e;x;y]\mwedge{}loc2[y]=loc(e)
unless loc(e) \mmember{} f \mmember{} \mBbbP{})
Date html generated:
2015_07_21-PM-04_27_14
Last ObjectModification:
2015_01_27-PM-05_14_54
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