Nuprl Lemma : prior-imax-class-lb2
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[n:ℕ]. ∀[A:Type]. ∀[f:A ⟶ ℕ]. ∀[Z:EClass(A)].
uiff(if e ∈b ((maximum f[x] ≥ 0 with x from Z))' then ((maximum f[x] ≥ 0 with x from Z))'(e) else -1 fi
≤ n;∀[e':E(Z)]. f[Z(e')] ≤ n supposing e' ≤loc e )
supposing ¬↑e ∈b Z
Proof
Definitions occuring in Statement :
es-prior-val: (X)',
imax-class: (maximum f[v] ≥ lb with v from X),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-E: E,
nat: ℕ,
assert: ↑b,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
le: A ≤ B,
not: ¬A,
function: x:A ⟶ B[x],
minus: -n,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
nat: ℕ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
es-E-interface: E(X),
top: Top,
true: True,
le: A ≤ B,
not: ¬A,
ge: i ≥ j ,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B,
es-locl: (e <loc e'),
es-le: e ≤loc e'
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[n:\mBbbN{}]. \mforall{}[A:Type]. \mforall{}[f:A {}\mrightarrow{} \mBbbN{}]. \mforall{}[Z:EClass(A)].
uiff(if e \mmember{}\msubb{} ((maximum f[x] \mgeq{} 0 with x from Z))'
then ((maximum f[x] \mgeq{} 0 with x from Z))'(e)
else -1
fi \mleq{} n;\mforall{}[e':E(Z)]. f[Z(e')] \mleq{} n supposing e' \mleq{}loc e )
supposing \mneg{}\muparrow{}e \mmember{}\msubb{} Z
Date html generated:
2016_05_17-AM-07_02_27
Last ObjectModification:
2016_01_17-PM-06_56_59
Theory : event-ordering
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