Nuprl Lemma : last-event-of-set
∀es:EO. ∀n:ℕ+. ∀f:ℕn ⟶ E. ∃k:ℕn. ∀i:ℕn. f i ≤loc f k supposing ∀i,j:ℕn. (loc(f i) = loc(f j) ∈ Id)
Proof
Definitions occuring in Statement :
es-le: e ≤loc e' ,
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
int_seg: {i..j-},
nat_plus: ℕ+,
uimplies: b supposing a,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat_plus: ℕ+,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
so_apply: x[s],
exists: ∃x:A. B[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
less_than: a < b,
squash: ↓T,
true: True,
decidable: Dec(P),
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}es:EO. \mforall{}n:\mBbbN{}\msupplus{}. \mforall{}f:\mBbbN{}n {}\mrightarrow{} E. \mexists{}k:\mBbbN{}n. \mforall{}i:\mBbbN{}n. f i \mleq{}loc f k supposing \mforall{}i,j:\mBbbN{}n. (loc(f i) = loc(f j))
Date html generated:
2016_05_16-AM-09_28_49
Last ObjectModification:
2016_01_17-PM-01_32_06
Theory : new!event-ordering
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