Nuprl Lemma : fpf-join-is-empty
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[f,g:x:A fp-> Top]. (fpf-is-empty(f ⊕ g) ~ fpf-is-empty(f) ∧b fpf-is-empty(g))
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-is-empty: fpf-is-empty(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
band: p ∧b q,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
fpf: a:A fp-> B[a],
fpf-is-empty: fpf-is-empty(f),
fpf-join: f ⊕ g,
pi1: fst(t),
fpf-dom: x ∈ dom(f),
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s],
or: P ∨ Q,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
bfalse: ff,
eq_int: (i =z j),
band: p ∧b q,
btrue: tt,
cons: [a / b],
l_all: (∀x∈L.P[x]),
assert: ↑b,
true: True,
prop: ℙ,
deq: EqDecider(T),
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
and: P ∧ Q,
eqof: eqof(d),
iff: P ⇐⇒ Q,
ge: i ≥ j ,
decidable: Dec(P),
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
rev_implies: P ⇐ Q,
nequal: a ≠ b ∈ T
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f,g:x:A fp-> Top].
(fpf-is-empty(f \moplus{} g) \msim{} fpf-is-empty(f) \mwedge{}\msubb{} fpf-is-empty(g))
Date html generated:
2016_05_16-AM-11_10_57
Last ObjectModification:
2016_01_17-PM-03_48_35
Theory : event-ordering
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