{ 
[A,C,B:Type]. [eqa:EqDecider(A)]. [eqc,eqc':EqDecider(C)]. [r:A 
C].
[f:a:A fp-> B]. [a:A]. [z:B].
rename(r;f)(r a)?z = f(a)?z supposing Inj(A;C;r) }
{ Proof }
Definitions occuring in Statement :
fpf-rename: rename(r;f),
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
inject: Inj(A;B;f),
uimplies: b supposing a,
uall: [x:A]. B[x],
apply: f a,
function: x:A B[x],
universe: Type,
equal: s = t,
deq: EqDecider(T)
Definitions :
so_lambda: 
x.t[x],
member: t 
T,
not: 
A,
implies: P 
Q,
false: False,
so_apply: x[s],
all: x:A. B[x]
Lemmas :
top_wf,
fpf_wf,
fpf-trivial-subtype-top
\mforall{}[A,C,B:Type]. \mforall{}[eqa:EqDecider(A)]. \mforall{}[eqc,eqc':EqDecider(C)]. \mforall{}[r:A {}\mrightarrow{} C]. \mforall{}[f:a:A fp-> B]. \mforall{}[a:A].
\mforall{}[z:B].
rename(r;f)(r a)?z = f(a)?z supposing Inj(A;C;r)
Date html generated:
2011_08_10-AM-08_04_45
Last ObjectModification:
2011_06_18-AM-08_22_46
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