Nuprl Lemma : fpf-join-cap-sq
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[f,g:a:A fp-> Top]. ∀[x:A]. ∀[z:Top].
(f ⊕ g(x)?z ~ if x ∈ dom(f) then f(x)?z else g(x)?z fi )
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-cap: f(x)?z,
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
fpf-cap: f(x)?z,
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
assert: ↑b,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bfalse: ff,
bnot: ¬bb,
false: False,
iff: P ⇐⇒ Q,
or: P ∨ Q,
not: ¬A,
rev_implies: P ⇐ Q,
prop: ℙ,
guard: {T}
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f,g:a:A fp-> Top]. \mforall{}[x:A]. \mforall{}[z:Top].
(f \moplus{} g(x)?z \msim{} if x \mmember{} dom(f) then f(x)?z else g(x)?z fi )
Date html generated:
2016_05_16-AM-11_11_18
Last ObjectModification:
2015_12_29-AM-09_17_48
Theory : event-ordering
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