{ 
[Info:Type]
es:EO+(Info). X:EClass(Top). f:sys-antecedent(es;X).
[R:E(X) 
E(X) 
]
(Refl(E(X);a,b.R[a;b])
Trans(E(X);a,b.R[a;b])
(b:E(X). R[f b;b] supposing 
(loc(f b) = loc(b)))
(a,b:E(X). ((a <loc b) R[a;b]))
(a,b:E(X). R[a;b] supposing a 
(X;f) b)) }
{ Proof }
Definitions occuring in Statement :
cut-order: a (X;f) b,
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-loc: loc(e),
Id: Id,
trans: Trans(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y]),
uimplies: b supposing a,
uall: [x:A]. B[x],
top: Top,
prop: ,
so_apply: x[s1;s2],
all: x:A. B[x],
not: A,
implies: P Q,
apply: f a,
function: x:A B[x],
universe: Type,
equal: s = t
Definitions :
record: record(x.T[x]),
union: left + right,
es-causl: (e < e'),
bool: 
,
top: Top,
lambda: 
x.A[x],
fpf: a:A fp-> B[a],
record-select: r.x,
limited-type: LimitedType,
es-loc: loc(e),
es-E: E,
subtype: S 
T,
strong-subtype: strong-subtype(A;B),
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
set: {x:A| B[x]} ,
dep-isect: Error :dep-isect,
record+: record+,
le: A B,
ge: i 
j ,
less_than: a < b,
product: x:A 
B[x],
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
void: Void,
false: False,
member: t 
T,
true: True,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
assert: 
b,
fset-member: a s,
cut-order: a (X;f) b,
event_ordering: EO,
es-locl: (e <loc e'),
Id: Id,
equal: s = t,
not: A,
trans: Trans(T;x,y.E[x; y]),
event-ordering+: EO+(Info),
eclass: EClass(A[eo; e]),
sys-antecedent: sys-antecedent(es;Sys),
uall: [x:A]. B[x],
es-E-interface: E(X),
all: x:A. B[x],
uimplies: b supposing a,
isect: 
x:A. B[x],
apply: f a,
prop: ,
universe: Type,
implies: P Q,
function: x:A B[x],
refl: Refl(T;x,y.E[x; y]),
so_lambda: 
x y.t[x; y],
so_apply: x[s1;s2],
RepeatFor: Error :RepeatFor,
MaAuto: Error :MaAuto,
CollapseTHEN: Error :CollapseTHEN,
Auto: Error :Auto,
tactic: Error :tactic,
in-eclass: e 
X,
es-prior-interface: prior(X),
eclass-val: X(e),
cand: A c B,
iff: P 
Q,
rel_plus: R
,
infix_ap: x f y,
es-cut: Cut(X;f),
fset: FSet{T},
cut-of: cut(X;f;s),
deq-member: deq-member(eq;x;L),
or: P 
Q,
guard: {T},
l_member: (x l),
so_apply: x[s],
so_lambda: x.t[x],
Try: Error :Try,
THENL_cons: Error :THENL_nil,
THENL_cons: Error :THENL_cons,
CollapseTHENM: Error :CollapseTHENM,
THENL_v2: Error :THENL,
label: ...$L... t,
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
pair: <a, b>,
sq_type: SQType(T),
es-causle: e c e',
es-le: e loc e' ,
rev_implies: P Q,
exists: 
x:A. B[x]
Lemmas :
es-locl_irreflexivity,
es-le_weakening_eq,
es-locl_transitivity2,
cut-order-prior,
es-prior-interface_wf,
eclass-val_wf2,
eclass-val_wf,
es-prior-interface-val,
cut-order-step,
subtype_base_sq,
set_subtype_base,
es-causl_transitivity2,
es-causl_irreflexivity,
es-base-E_wf,
subtype_rel_self,
es-causle_wf,
es-causle_weakening_eq,
ifthenelse_wf,
false_wf,
fset-member_wf,
cut-of_wf,
true_wf,
deq-member_wf,
uiff_inversion,
cut-order-induction,
cut-order-iff,
es-E-interface_wf,
refl_wf,
trans_wf,
member_wf,
es-E_wf,
subtype_rel_wf,
es-loc_wf,
event-ordering+_inc,
Id_wf,
not_wf,
es-locl_wf,
cut-order_wf,
cut-order_witness,
sys-antecedent_wf,
eclass_wf,
event-ordering+_wf,
top_wf,
es-causl_wf,
assert_wf,
es-E-interface-subtype_rel
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}f:sys-antecedent(es;X).
\mforall{}[R:E(X) {}\mrightarrow{} E(X) {}\mrightarrow{} \mBbbP{}]
(Refl(E(X);a,b.R[a;b])
{}\mRightarrow{} Trans(E(X);a,b.R[a;b])
{}\mRightarrow{} (\mforall{}b:E(X). R[f b;b] supposing \mneg{}(loc(f b) = loc(b)))
{}\mRightarrow{} (\mforall{}a,b:E(X). ((a <loc b) {}\mRightarrow{} R[a;b]))
{}\mRightarrow{} (\mforall{}a,b:E(X). R[a;b] supposing a \mleq{}(X;f) b))
Date html generated:
2011_08_16-PM-05_56_39
Last ObjectModification:
2011_06_20-AM-01_39_25
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