Nuprl Lemma : member-disjoint-union-comb
∀[Info,A,B:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. uiff(↑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,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
universe: Type
Lemmas :
bag-size-append,
bag-combine-single-right-as-map,
bag-size-map,
iff_transitivity,
assert_wf,
bor_wf,
bnot_wf,
eq_int_wf,
bag-size_wf,
class-ap_wf,
nat_wf,
or_wf,
not_wf,
equal-wf-T-base,
iff_weakening_uiff,
assert_of_bor,
assert_of_bnot,
assert_of_eq_int,
decidable__int_equal,
assert_witness,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
decidable__equal_int
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} X (+) Y;\muparrow{}(e \mmember{}\msubb{} X \mvee{}\msubb{}e \mmember{}\msubb{} Y))
Date html generated:
2015_07_23-AM-11_27_00
Last ObjectModification:
2015_01_28-PM-11_15_02
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