Nuprl Lemma : l_all-mapfilter-interface-predecessors
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[X:EClass(A)]. ∀[Q:E(X) ─→ 𝔹]. ∀[P:A ─→ 𝔹]. ∀[e:E(X)].
uiff((∀v∈mapfilter(λe.X(e);λe'.Q[e'];≤(X)(e)).↑P[v]);∀e'≤e.(↑e' ∈b X) ⇒ (↑Q[e']) ⇒ (↑P[X(e')]))
Proof
Definitions occuring in Statement :
es-interface-predecessors: ≤(X)(e),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
alle-le: ∀e≤e'.P[e],
mapfilter: mapfilter(f;P;L),
l_all: (∀x∈L.P[x]),
assert: ↑b,
bool: 𝔹,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
so_apply: x[s],
implies: P ⇒ Q,
lambda: λx.A[x],
function: x:A ─→ B[x],
universe: Type
Lemmas :
bool_wf,
es-E-interface_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
top_wf,
eclass_wf,
event-ordering+_wf,
assert_witness,
eclass-val_wf,
assert_wf,
in-eclass_wf,
es-le_wf,
l_all_wf2,
mapfilter_wf,
Id_wf,
es-loc_wf,
es-interface-predecessors_wf,
set_wf,
sq_stable__assert,
l_member_wf,
select_wf,
sq_stable__le,
int_seg_wf,
length_wf,
alle-le_wf,
l_all_iff,
member-mapfilter,
es-le-loc,
member-interface-predecessors-subtype,
assert_functionality_wrt_uiff
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Q:E(X) {}\mrightarrow{} \mBbbB{}]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[e:E(X)].
uiff((\mforall{}v\mmember{}mapfilter(\mlambda{}e.X(e);\mlambda{}e'.Q[e'];\mleq{}(X)(e)).\muparrow{}P[v]);\mforall{}e'\mleq{}e.(\muparrow{}e' \mmember{}\msubb{} X) {}\mRightarrow{} (\muparrow{}Q[e']) {}\mRightarrow{} (\muparrow{}P[X(e')]))
Date html generated:
2015_07_21-PM-03_39_55
Last ObjectModification:
2015_01_27-PM-06_31_47
Home
Index