Nuprl Lemma : fpf-join-range
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[df:x:A fp-> Type]. ∀[f:x:A fp-> df(x)?Top]. ∀[dg:x:A fp-> Type].
∀[g:x:A fp-> dg(x)?Top].
(f ⊕ g ∈ x:A fp-> df ⊕ dg(x)?Top) supposing
((∀x:A. ((↑x ∈ dom(g)) ⇒ (↑x ∈ dom(dg)))) and
(∀x:A. ((↑x ∈ dom(f)) ⇒ (↑x ∈ dom(df)))) and
df || dg)
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-compatible: f || g,
fpf-cap: f(x)?z,
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
fpf-join: f ⊕ g,
fpf: a:A fp-> B[a],
fpf-dom: x ∈ dom(f),
pi1: fst(t),
fpf-cap: f(x)?z,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
squash: ↓T,
true: True,
fpf-compatible: f || g,
cand: A c∧ B
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[df:x:A fp-> Type]. \mforall{}[f:x:A fp-> df(x)?Top]. \mforall{}[dg:x:A fp-> Type].
\mforall{}[g:x:A fp-> dg(x)?Top].
(f \moplus{} g \mmember{} x:A fp-> df \moplus{} dg(x)?Top) supposing
((\mforall{}x:A. ((\muparrow{}x \mmember{} dom(g)) {}\mRightarrow{} (\muparrow{}x \mmember{} dom(dg)))) and
(\mforall{}x:A. ((\muparrow{}x \mmember{} dom(f)) {}\mRightarrow{} (\muparrow{}x \mmember{} dom(df)))) and
df || dg)
Date html generated:
2016_05_16-AM-11_11_36
Last ObjectModification:
2016_01_17-PM-03_49_44
Theory : event-ordering
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