{ 
[A,C,B:Type]. [eqa:EqDecider(A)]. [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 :
member: t 
T,
prop: 
,
so_lambda: 
x.t[x],
uall: [x:A]. B[x],
uimplies: b supposing a,
fpf-cap: f(x)?z,
ifthenelse: if b then t else f fi ,
all: x:A. B[x],
implies: P 
Q,
btrue: tt,
bfalse: ff,
exists: 
x:A. B[x],
cand: A c
B,
so_apply: x[s],
bool: 
,
unit: Unit,
iff: P 
Q,
and: P Q,
not: 
A,
false: False,
inject: Inj(A;B;f),
rev_implies: P Q,
it: 
,
guard: {T}
Lemmas :
bool_wf,
assert_wf,
fpf-dom_wf,
fpf-trivial-subtype-top,
fpf-rename-ap,
not_wf,
bnot_wf,
iff_weakening_uiff,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
inject_wf,
fpf_wf,
deq_wf,
fpf-rename_wf,
fpf-rename-dom
\mforall{}[A,C,B:Type]. \mforall{}[eqa:EqDecider(A)]. \mforall{}[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_40
Last ObjectModification:
2011_06_18-AM-08_22_43
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