Nuprl Lemma : simple-comb2

{

[Info,A,B,C:Type].

F:bag(A)

bag(B)

bag(C)

[X:EClass(A)].

[Y:EClass(B)]. (

x,y.F[x;y]|X;Y|

EClass(C)) }

{ Proof }

Definitions occuring in Statement : simple-comb2:

x,y.F[x; y]|X;Y|, eclass: EClass(A[eo; e]), uall:

[x:A]. B[x], so_apply: x[s1;s2], all:

x:A. B[x], member: t

T, function: x:A

B[x], universe: Type, bag: bag(T)
Definitions : natural_number: $n, lambda:

x.A[x], select: l[i], cons: [car / cdr], nil: [], function: x:A

B[x], member: t

T, bag: bag(T), all:

x:A. B[x], isect:

x:A. B[x], universe: Type, uall:

[x:A]. B[x], equal: s = t, eclass: EClass(A[eo; e]), so_lambda:

x y.t[x; y], simple-comb2:

x,y.F[x; y]|X;Y|, so_apply: x[s1;s2], apply: f a, axiom: Ax, event-ordering+: EO+(Info), es-E: E, event_ordering: EO, record+: record+, dep-isect: Error :dep-isect, record-select: r.x, ifthenelse: if b then t else f fi , eq_atom: x =a y, token: "$token", es-base-E: es-base-E(es), top: Top, atom: Atom, eq_atom: eq_atom$n(x;y), subtype_rel: A

r B, subtype: S

T, bool:

, simple-comb: simple-comb(F;Xs), uimplies: b supposing a, fpf: a:A fp-> B[a], uiff: uiff(P;Q), and: P

Q, product: x:A

B[x], less_than: a < b, not:

A, ge: i

j , le: A

B, strong-subtype: strong-subtype(A;B), int:

, nat:

, rationals:

, real:

, set: {x:A| B[x]} , false: False, implies: P

Q, void: Void, prop:

, p-outcome: Outcome, int_seg: {i..j

}, list: type List, length: ||as||, label: ...$L... t, lelt: i

j < k, sq_type: SQType(T), tactic: Error :tactic, Try: Error :Try, CollapseTHEN: Error :CollapseTHEN, Auto: Error :Auto, same-thread: same-thread(es;p;e;e'), decidable: Dec(P), es-E-interface: E(X), collect-event: Error :collect-event, cut-order: Error :cut-order, path-goes-thru: Error :path-goes-thru, es-r-immediate-pred: es-r-immediate-pred(es;R;e';e), exists:

x:A. B[x], es-fset-loc: i

locs(s), existse-between3:

e

(e1,e2].P[e], existse-between2:

e

[e1,e2].P[e], alle-between2:

e

[e1,e2].P[e], existse-between1:

e

[e1,e2).P[e], alle-between1:

e

[e1,e2).P[e], alle-le:

e

e'.P[e], alle-lt:

e<e'.P[e], existse-le:

e

e'.P[e], existse-before:

e<e'.P[e], es-causle: e c

e', es-le: e

loc e' , es-locl: (e <loc e'), es-causl: (e < e'), infix_ap: x f y, consensus-rcv: consensus-rcv(V;A), cs-precondition: state s may consider v in inning i, cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i, cs-inning-committable: in state s, inning i could commit v , cs-inning-committed: in state s, inning i has committed v, cs-passed: by state s, a passed inning i without archiving a value, cs-archived: by state s, a archived v in inning i, cs-not-completed: in state s, a has not completed inning i, consensus-state3: consensus-state3(T), l_disjoint: l_disjoint(T;l1;l2), MaName: MaName, Knd: Knd, IdLnk: IdLnk, Id: Id, fset-closed: (s closed under fs), fset: FSet{T}, f-subset: xs

ys, fset-member: a

s, dstype: dstype(TypeNames; d; a), i-closed: i-closed(I), i-finite: i-finite(I), atom: Atom$n, sq_exists:

x:{A| B[x]}, q-rel: q-rel(r;x), qless: r < s, qle: r

s, limited-type: LimitedType, fun-connected: y is f*(x), l_all: (

x

L.P[x]), l_exists: (

x

L. P[x]), squash:

T, prime: prime(a), reducible: reducible(a), inject: Inj(A;B;f), cmp-le: cmp-le(cmp;x;y), l_contains: A

B, nat_plus:

, or: P

Q, union: left + right, guard: {T}
Lemmas : int_subtype_base, decidable__equal_int, subtype_base_sq, es-interface-top, subtype_rel_wf, top_wf, length_wf1, non_neg_length, length_cons, length_nil, length_wf_nat, select_wf, int_seg_wf, nat_wf, false_wf, not_wf, le_wf, simple-comb_wf, member_wf, bag_wf, eclass_wf, es-E_wf, es-base-E_wf, subtype_rel_self, event-ordering+_inc, event-ordering+_wf

\mforall{}[Info,A,B,C:Type]. \mforall{}F:bag(A) {}\mrightarrow{} bag(B) {}\mrightarrow{} bag(C). \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. (\mlambda{}x,y.F[x;y]|X;Y| \mmember{} EClass(C)) Date html generated: 2011_08_16-PM-04_57_28 Last ObjectModification: 2011_05_11-AM-01_29_11 Home Index