Nuprl Lemma : compose-fpf-dom
∀[A:Type]. ∀[B:A ⟶ Type].
∀f:x:A fp-> B[x]
∀[C:Type]
∀a:A ⟶ (C?). ∀b:C ⟶ A. ∀y:C.
((y ∈ fpf-domain(compose-fpf(a;b;f))) ⇐⇒ ∃x:A. ((x ∈ fpf-domain(f)) ∧ ((↑isl(a x)) c∧ (y = outl(a x) ∈ C))))
Proof
Definitions occuring in Statement :
compose-fpf: compose-fpf(a;b;f),
fpf-domain: fpf-domain(f),
fpf: a:A fp-> B[a],
l_member: (x ∈ l),
outl: outl(x),
assert: ↑b,
isl: isl(x),
uall: ∀[x:A]. B[x],
cand: A c∧ B,
so_apply: x[s],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
unit: Unit,
apply: f a,
function: x:A ⟶ B[x],
union: left + right,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
fpf: a:A fp-> B[a],
fpf-domain: fpf-domain(f),
compose-fpf: compose-fpf(a;b;f),
pi1: fst(t),
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
cand: A c∧ B,
uimplies: b supposing a,
rev_implies: P ⇐ Q,
isl: isl(x),
outl: outl(x),
not: ¬A,
false: False,
exists: ∃x:A. B[x]
Latex:
\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. \mforall{}y:C.
((y \mmember{} fpf-domain(compose-fpf(a;b;f)))
\mLeftarrow{}{}\mRightarrow{} \mexists{}x:A. ((x \mmember{} fpf-domain(f)) \mwedge{} ((\muparrow{}isl(a x)) c\mwedge{} (y = outl(a x)))))
Date html generated:
2016_05_16-AM-11_27_35
Last ObjectModification:
2015_12_29-AM-09_24_18
Theory : event-ordering
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