{ 
[Info:Type]
es:EO+(Info)
[Qa,Rb,Sc:E 
E 
]. [A,B,C:Type].
Ia:EClass(A). Ib:EClass(B). Ic:EClass(C). f1:E(Ia) B. f2:B C.
g1:E(Ib) E(Ia). g2:E(Ic) E(Ib).
((g1 glues Ia:Qa f1 Ib:Rb
g2 glues Ib:Rb 
e.(f2 Ib(e)) Ic:Sc)
g1 o g2 glues Ia:Qa f2 o f1 Ic:Sc) }
{ Proof }
Definitions occuring in Statement :
Q-R-glues: g glues Ia:Qa f Ib:Rb,
es-E-interface: E(X),
eclass-val: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
compose: f o g,
uall: [x:A]. B[x],
prop: ,
all: x:A. B[x],
implies: P Q,
and: P Q,
apply: f a,
lambda: x.A[x],
function: x:A B[x],
universe: Type
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
prop: ,
implies: P Q,
and: P Q,
Q-R-glues: g glues Ia:Qa f Ib:Rb,
compose: f o g,
cand: A c B,
es-interface-predicate: {I},
assert: 
b,
member: t 
T,
subtype: S 
T,
suptype: suptype(S; T),
so_lambda: 
x y.t[x; y],
btrue: tt,
ifthenelse: if b then t else f fi ,
true: True,
es-E-interface: E(X),
inject: Inj(A;B;f),
so_apply: x[s1;s2],
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T}
Lemmas :
es-E-interface_wf,
Q-R-glues_wf,
es-E-interface-subtype,
eclass-val_wf,
es-E_wf,
event-ordering+_inc,
event-ordering+_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eclass_wf,
assert_elim,
in-eclass_wf,
weak-antecedent-surjections-compose,
assert_wf,
es-interface-top,
Q-R-pre-preserving-compose,
strong-subtype-self,
inject-composes
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[Qa,Rb,Sc:E {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}]. \mforall{}[A,B,C:Type].
\mforall{}Ia:EClass(A). \mforall{}Ib:EClass(B). \mforall{}Ic:EClass(C). \mforall{}f1:E(Ia) {}\mrightarrow{} B. \mforall{}f2:B {}\mrightarrow{} C. \mforall{}g1:E(Ib) {}\mrightarrow{} E(Ia).
\mforall{}g2:E(Ic) {}\mrightarrow{} E(Ib).
((g1 glues Ia:Qa {}{}f1{}\mrightarrow{} Ib:Rb \mwedge{} g2 glues Ib:Rb {}{}\mlambda{}e.(f2 Ib(e)){}\mrightarrow{} Ic:Sc)
{}\mRightarrow{} g1 o g2 glues Ia:Qa {}{}f2 o f1{}\mrightarrow{} Ic:Sc)
Date html generated:
2011_08_16-PM-05_57_54
Last ObjectModification:
2011_06_20-AM-01_40_43
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