{ 
[A,A':Type].
[B:A 
Type]. [C:A' Type]. [eq:EqDecider(A)]. [eq':EqDecider(A')].
[f,g:a:A fp-> B[a]].
(f 
g) supposing (f g and (a:A. (B[a] r C[a])))
supposing strong-subtype(A;A') }
{ Proof }
Definitions occuring in Statement :
fpf-sub: f g,
fpf: a:A fp-> B[a],
subtype_rel: A r B,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
all: x:A. B[x],
function: x:A B[x],
universe: Type,
deq: EqDecider(T),
strong-subtype: strong-subtype(A;B)
Definitions :
so_lambda: 
x.t[x],
member: t 
T,
so_apply: x[s],
prop: 
,
implies: P 
Q,
all: x:A. B[x]
Lemmas :
fpf-ap_wf
\mforall{}[A,A':Type].
\mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[C:A' {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[eq':EqDecider(A')]. \mforall{}[f,g:a:A fp-> B[a]].
(f \msubseteq{} g) supposing (f \msubseteq{} g and (\mforall{}a:A. (B[a] \msubseteq{}r C[a])))
supposing strong-subtype(A;A')
Date html generated:
2011_08_10-AM-07_57_13
Last ObjectModification:
2011_06_18-AM-08_17_32
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