Nuprl Lemma : compose-fpf_wf
[A:Type]. [B:A 
Type]. [f:x:A fp-> B[x]]. [C:Type]. [a:A (C?)]. [b:C A].
compose-fpf(a;b;f) 
y:C fp-> B[b y] supposing y:A. ((
isl(a y)) 
((b outl(a y)) = y))
Proof not projected
Definitions occuring in Statement :
compose-fpf: compose-fpf(a;b;f),
fpf: a:A fp-> B[a],
outl: outl(x),
isl: isl(x),
assert: b,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
all: x:A. B[x],
implies: P Q,
unit: Unit,
member: t T,
apply: f a,
function: x:A B[x],
union: left + right,
universe: Type,
equal: s = t
Definitions :
uall: [x:A]. B[x],
fpf: a:A fp-> B[a],
so_apply: x[s],
uimplies: b supposing a,
implies: P Q,
member: t T,
compose-fpf: compose-fpf(a;b;f),
fpf-domain: fpf-domain(f),
compose: f o g,
pi2: snd(t),
so_lambda: 
x.t[x],
squash: 
T,
true: True,
prop: 
,
pi1: fst(t),
all: x:A. B[x],
sq_stable: SqStable(P),
exists: 
x:A. B[x],
and: P 
Q,
cand: A c B,
iff: P 
Q,
guard: {T}
Lemmas :
mapfilter_wf,
fpf-domain_wf,
fpf-trivial-subtype-top,
isl_wf,
unit_wf2,
outl_wf,
sq_stable__assert,
assert_wf,
member_map_filter,
l_member_wf,
all_wf,
equal_wf,
fpf_wf,
squash_wf,
true_wf
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:x:A fp-> B[x]]. \mforall{}[C:Type]. \mforall{}[a:A {}\mrightarrow{} (C?)]. \mforall{}[b:C {}\mrightarrow{} A].
compose-fpf(a;b;f) \mmember{} y:C fp-> B[b y] supposing \mforall{}y:A. ((\muparrow{}isl(a y)) {}\mRightarrow{} ((b outl(a y)) = y))
Date html generated:
2012_01_23-AM-11_55_17
Last ObjectModification:
2011_12_28-PM-12_07_43
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