{ 
[A:Type]. [B:A 
Type].
eq:EqDecider(A). f,g:a:A fp-> B[a]. x:A.
[P:a:A B[a] 
]
z != f(x) ==> P[x;z] 
z != g(x) ==> P[x;z] supposing g 
f }
{ Proof }
Definitions occuring in Statement :
fpf-sub: f g,
fpf-val: z != f(x) ==> P[a; z],
fpf: a:A fp-> B[a],
uimplies: b supposing a,
uall: [x:A]. B[x],
prop: ,
so_apply: x[s1;s2],
so_apply: x[s],
all: x:A. B[x],
implies: P Q,
function: x:A B[x],
universe: Type,
deq: EqDecider(T)
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
so_apply: x[s],
prop: ,
uimplies: b supposing a,
fpf-sub: f g,
implies: P Q,
fpf-val: z != f(x) ==> P[a; z],
so_apply: x[s1;s2],
cand: A c
B,
member: t 
T,
so_lambda: 
x.t[x]
Lemmas :
pair_wf,
assert_wf,
fpf-dom_wf,
fpf-trivial-subtype-top,
assert_witness,
fpf-ap_wf,
fpf_wf,
deq_wf
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type].
\mforall{}eq:EqDecider(A). \mforall{}f,g:a:A fp-> B[a]. \mforall{}x:A.
\mforall{}[P:a:A {}\mrightarrow{} B[a] {}\mrightarrow{} \mBbbP{}]. z != f(x) ==> P[x;z] {}\mRightarrow{} z != g(x) ==> P[x;z] supposing g \msubseteq{} f
Date html generated:
2011_08_10-AM-08_02_15
Last ObjectModification:
2011_06_18-AM-08_20_19
Home
Index