{ 
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} .
(e:E. Dec(Q1 e))
(e:E. Dec(Q2 e))
Q1 
= f== P1
Q2 = g== P2
e.((Q1 e) 
(Q2 e)) = [P1? f : g]== e.((P1 e) (P2 e))
supposing e:E. ((P1 e) (
(P2 e))) }
{ Proof }
Definitions occuring in Statement :
weak-antecedent-surjection: Q = f== P,
conditional: [P? f : g],
es-E: E,
event_ordering: EO,
decidable: Dec(P),
uimplies: b supposing a,
uall: [x:A]. B[x],
prop: ,
all: x:A. B[x],
not: A,
implies: P Q,
or: 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: ,
uimplies: b supposing a,
implies: P Q,
not: A,
weak-antecedent-surjection: Q = f== P,
member: t 
T,
false: False,
and: P 
Q,
subtype: S 
T,
suptype: suptype(S; T),
or: P Q,
exists: 
x:A. B[x],
conditional: [P? f : g],
branch: if p:P then A[p] else B fi ,
guard: {T},
cand: A c B,
decidable: Dec(P)
Lemmas :
es-E_wf,
weak-antecedent-surjection_wf,
decidable_wf,
not_wf,
event_ordering_wf,
weak-antecedent-conditional,
decidable__or
\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\} .
(\mforall{}e:E. Dec(Q1 e))
{}\mRightarrow{} (\mforall{}e:E. Dec(Q2 e))
{}\mRightarrow{} Q1 \mleftarrow{}\mleftarrow{}= f== P1
{}\mRightarrow{} Q2 \mleftarrow{}\mleftarrow{}= g== P2
{}\mRightarrow{} \mlambda{}e.((Q1 e) \mvee{} (Q2 e)) \mleftarrow{}\mleftarrow{}= [P1? f : g]== \mlambda{}e.((P1 e) \mvee{} (P2 e))
supposing \mforall{}e:E. ((P1 e) {}\mRightarrow{} (\mneg{}(P2 e)))
Date html generated:
2011_08_16-AM-11_07_25
Last ObjectModification:
2011_06_18-AM-09_40_47
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