{ 
[es:EO]. [P:E 
]. [Q,R:E E ]. [f:{e:E| P e} E].
(Inj({e:E| P e} ;E;f)) supposing
(f is Q-R-pre-preserving on P and
AntiSym(E;e,e'.R e e') and
Refl(E;e,e'.Q e e')) }
{ Proof }
Definitions occuring in Statement :
Q-R-pre-preserving: f is Q-R-pre-preserving on P,
es-E: E,
event_ordering: EO,
anti_sym: AntiSym(T;x,y.R[x; y]),
refl: Refl(T;x,y.E[x; y]),
inject: Inj(A;B;f),
uimplies: b supposing a,
uall: [x:A]. B[x],
prop: ,
set: {x:A| B[x]} ,
apply: f a,
function: x:A B[x]
Definitions :
uall: [x:A]. B[x],
prop: ,
uimplies: b supposing a,
refl: Refl(T;x,y.E[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
Q-R-pre-preserving: f is Q-R-pre-preserving on P,
inject: Inj(A;B;f),
all: x:A. B[x],
implies: P 
Q,
member: t 
T,
and: P 
Q,
cand: A c B,
guard: {T}
Lemmas :
es-E_wf,
event_ordering_wf
\mforall{}[es:EO]. \mforall{}[P:E {}\mrightarrow{} \mBbbP{}]. \mforall{}[Q,R:E {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}]. \mforall{}[f:\{e:E| P e\} {}\mrightarrow{} E].
(Inj(\{e:E| P e\} ;E;f)) supposing
(f is Q-R-pre-preserving on P and
AntiSym(E;e,e'.R e e') and
Refl(E;e,e'.Q e e'))
Date html generated:
2011_08_16-AM-11_07_59
Last ObjectModification:
2011_06_18-AM-09_41_23
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