Nuprl Lemma : interface-part-val
∀[Info,T:Type]. ∀[X:EClass(T)]. ∀[g:∩es:EO+(Info). (E(X) ─→ Id)]. ∀[i:Id]. ∀[es:EO+(Info)]. ∀[e:E].
(X|g=i)(e) ~ X(e) supposing ↑e ∈b (X|g=i)
Proof
Definitions occuring in Statement :
es-interface-part: (X|g=i),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
isect: ∩x:A. B[x],
function: x:A ─→ B[x],
universe: Type,
sqequal: s ~ t
Lemmas :
is-interface-part,
in-eclass_wf,
bool_wf,
eqtt_to_assert,
eq_id_wf,
assert-eq-id,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
assert_wf,
es-interface-part_wf,
top_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
Id_wf,
es-E-interface_wf,
eclass_wf,
event-ordering+_wf
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[g:\mcap{}es:EO+(Info). (E(X) {}\mrightarrow{} Id)]. \mforall{}[i:Id]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
(X|g=i)(e) \msim{} X(e) supposing \muparrow{}e \mmember{}\msubb{} (X|g=i)
Date html generated:
2015_07_21-PM-04_20_19
Last ObjectModification:
2015_01_27-PM-05_17_15
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