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 ∈ A))
Proof
Definitions occuring in Statement :
compose-fpf: compose-fpf(a;b;f),
fpf: a:A fp-> B[a],
outl: outl(x),
assert: ↑b,
isl: isl(x),
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 ∈ T
Lemmas :
mapfilter_wf,
fpf-domain_wf,
subtype-fpf2,
top_wf,
subtype_top,
isl_wf,
unit_wf2,
assert_wf,
outl_wf,
member_map_filter,
l_member_wf,
squash_wf,
true_wf,
list_wf,
iff_weakening_equal,
all_wf,
assert_elim,
bfalse_wf,
and_wf,
equal_wf,
btrue_neq_bfalse,
fpf_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:
2015_07_17-AM-11_11_43
Last ObjectModification:
2015_02_04-PM-05_06_42
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