{ 
es:EO
[P1,Q1,P2,Q2:E 
].
dcd_P1:e:E Dec(P1 e). f:{e:E| P1 e} {e:E| Q1 e} .
g:{e:E| P2 e} {e:E| Q2 e} .
((Q1 
==f== P1 
Q2 ==g== P2)
e.((Q1 e) 
(Q2 e)) ==[P1? f : g]== e.((P1 e) (P2 e))) }
{ Proof }
Definitions occuring in Statement :
weak-antecedent-function: Q ==f== P,
conditional: [P? f : g],
es-E: E,
event_ordering: EO,
decidable: Dec(P),
uall: [x:A]. B[x],
prop: ,
all: x:A. B[x],
implies: P Q,
or: P Q,
and: P Q,
set: {x:A| B[x]} ,
apply: f a,
lambda: x.A[x],
function: x:A B[x]
Definitions :
all: x:A. B[x],
uall: [x:A]. B[x],
prop: ,
implies: P Q,
and: P Q,
member: t 
T,
subtype: S 
T,
suptype: suptype(S; T),
weak-antecedent-function: Q ==f== P,
or: P Q,
conditional: [P? f : g],
branch: if p:P then A[p] else B fi ,
guard: {T},
decidable: Dec(P),
not: 
A,
false: False
Lemmas :
weak-antecedent-function_wf,
es-E_wf,
decidable_wf,
event_ordering_wf
\mforall{}es:EO
\mforall{}[P1,Q1,P2,Q2:E {}\mrightarrow{} \mBbbP{}].
\mforall{}dcd$_{P1}$:e:E {}\mrightarrow{} Dec(P1 e). \mforall{}f:\{e:E| P1 e\} {}\mrightarrow{} \{e:E| Q1 e\} . \mforall{}g:\{e:E| P2 e\000C\} {}\mrightarrow{} \{e:E| Q2 e\} .
((Q1 \mleftarrow{}==f== P1 \mwedge{} Q2 \mleftarrow{}==g== P2) {}\mRightarrow{} \mlambda{}e.((Q1 e) \mvee{} (Q2 e)) \mleftarrow{}==[P1? f : g]== \mlambda{}e.((P1 e) \mvee{} (P2 e)))
Date html generated:
2011_08_16-AM-11_06_56
Last ObjectModification:
2011_06_18-AM-09_39_13
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