Nuprl Lemma : is-interface-part
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[T:Type]. ∀[X:EClass(T)]. ∀[g:E(X) ─→ Id]. ∀[i:Id]. ∀[e:E].
uiff(↑e ∈b (X|g=i);(↑e ∈b X) ∧ ((g e) = i ∈ Id))
Proof
Definitions occuring in Statement :
es-interface-part: (X|g=i),
es-E-interface: E(X),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
eq_int_wf,
bag-size_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eq_id_wf,
assert_wf,
assert-eq-id,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
nat_wf,
bag_size_empty_lemma,
false_wf,
assert_witness,
true_wf,
neg_assert_of_eq_int,
Id_wf,
es-E_wf,
event-ordering+_subtype,
bag_wf,
event-ordering+_wf
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[g:E(X) {}\mrightarrow{} Id]. \mforall{}[i:Id]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} (X|g=i);(\muparrow{}e \mmember{}\msubb{} X) \mwedge{} ((g e) = i))
Date html generated:
2015_07_20-PM-03_37_12
Last ObjectModification:
2015_01_27-PM-10_11_54
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