{ 
[A:Type]. [B:A 
Type]. [eq:EqDecider(A)]. [f1,g1,f2,g2:a:A fp-> B[a]].
(f1 
f2 
g1 g2) supposing (f2 g2 and f1 g1 and f2 || g1) }
{ Proof }
Definitions occuring in Statement :
fpf-join: f g,
fpf-compatible: f || g,
fpf-sub: f g,
fpf: a:A fp-> B[a],
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
function: x:A B[x],
universe: Type,
deq: EqDecider(T)
Definitions :
uall: [x:A]. B[x],
so_apply: x[s],
uimplies: b supposing a,
fpf-sub: f g,
member: t 
T,
all: x:A. B[x],
implies: P 
Q,
cand: A c
B,
prop: 
,
so_lambda: 
x.t[x],
or: P 
Q,
guard: {T},
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
top: Top,
and: P Q,
rev_implies: P 
Q,
iff: P Q,
not: 
A,
false: False,
bool: 
,
unit: Unit,
fpf-compatible: f || g,
it: 
Lemmas :
assert_wf,
fpf-dom_wf,
fpf-join_wf,
top_wf,
fpf-trivial-subtype-top,
pair_wf,
assert_witness,
fpf-sub_wf,
fpf-compatible_wf,
fpf_wf,
deq_wf,
fpf-join-dom,
not_wf,
bnot_wf,
bool_wf,
iff_weakening_uiff,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
fpf-join-ap-sq
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f1,g1,f2,g2:a:A fp-> B[a]].
(f1 \moplus{} f2 \msubseteq{} g1 \moplus{} g2) supposing (f2 \msubseteq{} g2 and f1 \msubseteq{} g1 and f2 || g1)
Date html generated:
2011_08_10-AM-08_00_40
Last ObjectModification:
2011_06_18-AM-08_19_35
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