{ [Info,A,B:Type]. [X:EClass(A)]. [Y:EClass(B)].
    ((X | Y))' = ((X)' | (Y)') supposing Singlevalued(X)  Singlevalued(Y) }

{ Proof }



Definitions occuring in Statement :  es-or-latest: (X | Y) es-prior-val: (X)' es-interface-or: (X | Y) sv-class: Singlevalued(X) eclass: EClass(A[eo; e]) uimplies: b supposing a uall: [x:A]. B[x] and: P  Q universe: Type equal: s = t one_or_both: one_or_both(A;B)
Definitions :  btrue: tt sq_type: SQType(T) es-prior-interface: prior(X) es-interface-at: X@i intensional-universe: IType eq_term: a == b valueall-type: valueall-type(T) sqequal: s ~ t dataflow: dataflow(A;B) b-union: A  B fpf-cap: f(x)?z record: record(x.T[x]) es-loc: loc(e) bool: true: True is_list_splitting: is_list_splitting(T;L;LL;L2;f) is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x) req: x = y rnonneg: rnonneg(r) rleq: x  y i-member: r  I partitions: partitions(I;p) modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f) fpf-sub: f  g sq_stable: SqStable(P) eclass-val: X(e) es-pred: pred(e) Id: Id int_seg: {i..j} divides: b | a assoced: a ~ b set_leq: a  b set_lt: a <p b grp_lt: a < b l_contains: A  B cmp-le: cmp-le(cmp;x;y) inject: Inj(A;B;f) reducible: reducible(a) prime: prime(a) squash: T l_exists: (xL. P[x]) l_all: (xL.P[x]) fun-connected: y is f*(x) qle: r  s qless: r < s q-rel: q-rel(r;x) sq_exists: x:{A| B[x]} list: type List i-finite: i-finite(I) i-closed: i-closed(I) p-outcome: Outcome fset-member: a  s f-subset: xs  ys fset-closed: (s closed under fs) l_disjoint: l_disjoint(T;l1;l2) cs-not-completed: in state s, a has not completed inning i cs-archived: by state s, a archived v in inning i cs-passed: by state s, a passed inning i without archiving a value cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i cs-precondition: state s may consider v in inning i cs-inning-committed: in state s, inning i has committed v cs-inning-committable: in state s, inning i could commit v  nat: es-le: e loc e'  es-causle: e c e' existse-before: e<e'.P[e] existse-le: ee'.P[e] alle-lt: e<e'.P[e] alle-le: ee'.P[e] alle-between1: e[e1,e2).P[e] existse-between1: e[e1,e2).P[e] alle-between2: e[e1,e2].P[e] existse-between2: e[e1,e2].P[e] existse-between3: e(e1,e2].P[e] es-fset-loc: i  locs(s) unit: Unit es-r-immediate-pred: es-r-immediate-pred(es;R;e';e) same-thread: same-thread(es;p;e;e') collect-event: collect-event(es;X;n;v.num[v];L.P[L];e) cut-order: a (X;f) b path-goes-thru: x-f*-y thru i decidable: Dec(P) so_apply: x[s] guard: {T} eq_knd: a = b l_member: (x  l) fpf-dom: x  dom(f) infix_ap: x f y es-causl: (e < e') cand: A c B es-E-interface: E(X) set: {x:A| B[x]}  decide: case b of inl(x) =s[x] | inr(y) =t[y] eq_atom: eq_atom$n(x;y) atom: Atom apply: f a es-base-E: es-base-E(es) token: "$token" eq_atom: x =a y ifthenelse: if b then t else f fi  record-select: r.x dep-isect: Error :dep-isect,  record+: record+ bag: bag(T) rev_implies: P  Q so_lambda: x.t[x] implies: P  Q union: left + right or: P  Q es-locl: (e <loc e') exists: x:A. B[x] subtype: S  T event_ordering: EO lambda: x.A[x] top: Top pair: <a, b> fpf: a:A fp-B[a] void: Void false: False strong-subtype: strong-subtype(A;B) le: A  B ge: i  j  not: A less_than: a < b uiff: uiff(P;Q) subtype_rel: A r B function: x:A  B[x] axiom: Ax one_or_both: one_or_both(A;B) prop: equal: s = t universe: Type uall: [x:A]. B[x] eclass: EClass(A[eo; e]) uimplies: b supposing a isect: x:A. B[x] member: t  T and: P  Q product: x:A  B[x] so_lambda: x y.t[x; y] sv-class: Singlevalued(X) es-prior-val: (X)' es-interface-or: (X | Y) in-eclass: e  X assert: b es-or-latest: (X | Y) iff: P  Q es-E: E all: x:A. B[x] event-ordering+: EO+(Info) cond-class: [X?Y] bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o} bag_size_single: bag_size_single{bag_size_single_compseq_tag_def:o}(x) one_or_both_ind_oobright: one_or_both_ind_oobright_compseq_tag_def oobright-rval: oobright-rval(x) one_or_both_ind_oobleft: one_or_both_ind_oobleft_compseq_tag_def oobleft-lval: oobleft-lval(x) oobboth?: oobboth?(x) oobleft?: oobleft?(x) oobright?: oobright?(x) one_or_both_ind_oobboth: one_or_both_ind_oobboth_compseq_tag_def oobboth-bval: oobboth-bval(x) natural_number: $n bag-size: bag-size(bs) limited-type: LimitedType bfalse: ff eq_bool: p =b q lt_int: i <z j le_int: i z j eq_int: (i = j) null: null(as) set_blt: a < b grp_blt: a < b dcdr-to-bool: [d] bl-all: (xL.P[x])_b bl-exists: (xL.P[x])_b b-exists: (i<n.P[i])_b eq_type: eq_type(T;T') qeq: qeq(r;s) q_less: q_less(r;s) q_le: q_le(r;s) deq-member: deq-member(eq;x;L) deq-disjoint: deq-disjoint(eq;as;bs) deq-all-disjoint: deq-all-disjoint(eq;ass;bs) eq_id: a = b eq_lnk: a = b es-eq-E: e = e' es-bless: e <loc e' es-ble: e loc e' bimplies: p  q band: p  q bor: p q bnot: b int: oob-apply: oob-apply(xs;ys) eclass-compose2: eclass-compose2(f;X;Y) es-latest-val: (X) oobright: oobright(rval) oobboth: oobboth(bval) oobleft: oobleft(lval) MaAuto: Error :MaAuto,  THEN: Error :THEN,  ParallelOp: Error :ParallelOp,  Auto: Error :Auto,  CollapseTHENA: Error :CollapseTHENA,  bag-only: only(bs) real: grp_car: |g| it: CollapseTHEN: Error :CollapseTHEN,  RepeatFor: Error :RepeatFor
Lemmas :  oobright_wf oobleft_wf bag_wf squash_wf set_subtype_base nat_wf bag-size_wf eq_int_wf assert_of_eq_int not_functionality_wrt_uiff bag-only_wf oobboth_wf es-le_wf is-latest-val or-latest-val interface-or-val es-latest-val_wf prior-val-as-latest-val prior-val-val product_subtype_base union_subtype_base es-prior-interface_wf1 es-prior-interface_wf es-E-interface_wf not_wf bnot_wf assert_of_bnot eqff_to_assert uiff_transitivity eqtt_to_assert le_wf es-interface-extensionality eclass-val_wf es-E_wf es-locl_wf assert_wf event-ordering+_wf all_functionality_wrt_iff iff_wf es-prior-val_wf one_or_both_wf es-or-latest_wf event-ordering+_inc eclass_wf sv-class_wf es-interface-or_wf iff_functionality_wrt_iff iff_transitivity is-prior-val exists_functionality_wrt_iff and_functionality_wrt_iff rev_implies_wf is-or-latest is-interface-or or_functionality_wrt_iff es-base-E_wf subtype_rel_self in-eclass_wf top_wf member_wf es-interface-top es-interface-subtype_rel2 subtype_rel_wf es-causl_wf Id_wf sq_stable__assert bool_wf intensional-universe_wf decidable__assert false_wf ifthenelse_wf true_wf subtype_base_sq bool_subtype_base assert_elim

\mforall{}[Info,A,B:Type].  \mforall{}[X:EClass(A)].  \mforall{}[Y:EClass(B)].
    ((X  |\msupminus{}  Y))'  =  ((X)'  |  (Y)')  supposing  Singlevalued(X)  \mwedge{}  Singlevalued(Y)


Date html generated: 2011_08_16-PM-06_10_19
Last ObjectModification: 2011_06_20-AM-01_48_45

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