Nuprl Lemma : member-disjoint-union-comb-bool
∀[Info,A,B:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. (e ∈b X (+) Y ~ e ∈b X ∨be ∈b Y)
Proof
Definitions occuring in Statement :
disjoint-union-comb: X (+) Y,
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
bor: p ∨bq,
uall: ∀[x:A]. B[x],
universe: Type,
sqequal: s ~ t
Lemmas :
bool_cases_sqequal,
member-eclass_wf,
disjoint-union-comb_wf,
sqequal-tt-to-assert,
bor_wf,
sqequal-ff-to-assert,
subtype_base_sq,
bool_wf,
bool_subtype_base,
btrue_wf,
ppcc-problem,
iff_imp_equal_bool,
member-disjoint-union-comb,
true_wf,
false_wf,
iff_weakening_equal,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
(e \mmember{}\msubb{} X (+) Y \msim{} e \mmember{}\msubb{} X \mvee{}\msubb{}e \mmember{}\msubb{} Y)
Date html generated:
2015_07_23-AM-11_27_03
Last ObjectModification:
2015_02_04-PM-04_45_12
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