{ 
[A:Type]. [B:A 
Type]. [f:a:A fp-> B[a]]. [eq:EqDecider(A)]. [x:A].
[P:a:{a:A| 
a 
dom(f)} B[a] 
].
(z != f(x) ==> P[x;z] ) }
{ Proof }
Definitions occuring in Statement :
fpf-val: z != f(x) ==> P[a; z],
fpf-dom: x dom(f),
fpf: a:A fp-> B[a],
assert: b,
uall: [x:A]. B[x],
prop: ,
so_apply: x[s1;s2],
so_apply: x[s],
member: t T,
set: {x:A| B[x]} ,
function: x:A B[x],
universe: Type,
deq: EqDecider(T)
Definitions :
uall: [x:A]. B[x],
so_apply: x[s],
prop: ,
member: t T,
fpf-val: z != f(x) ==> P[a; z],
so_apply: x[s1;s2],
implies: P 
Q,
so_lambda: 
x.t[x],
uimplies: b supposing a
Lemmas :
assert_wf,
fpf-dom_wf,
fpf-trivial-subtype-top,
fpf-ap_wf,
deq_wf,
fpf_wf
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:a:A fp-> B[a]]. \mforall{}[eq:EqDecider(A)]. \mforall{}[x:A]. \mforall{}[P:a:\{a:A| \muparrow{}a \mmember{} dom(f)\}
{}\mrightarrow{} B[a]
{}\mrightarrow{} \mBbbP{}].
(z != f(x) ==> P[x;z] \mmember{} \mBbbP{})
Date html generated:
2011_08_10-AM-07_56_37
Last ObjectModification:
2011_06_18-AM-08_17_18
Home
Index