Nuprl Lemma : es-fset-last_wf
∀[es:EO]. ∀[s:fset(E)]. ∀[i:Id].
s(i) ∈ {e:E| (loc(e) = i ∈ Id) ∧ e ∈ s ∧ (∀e':E. (e' ∈ s ⇒ (¬(e <loc e'))))} supposing i ∈ locs(s)
Proof
Definitions occuring in Statement :
es-fset-last: s(i),
es-fset-loc: i ∈ locs(s),
es-locl: (e <loc e'),
es-eq: es-eq(es),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
fset-member: a ∈ s,
fset: fset(T),
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
es-fset-last: s(i),
not: ¬A,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
top: Top,
es-fset-loc: i ∈ locs(s),
false: False,
prop: ℙ,
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
es-locl: (e <loc e'),
or: P ∨ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
subtract: n - m,
true: True,
cons: [a / b],
bfalse: ff,
int_seg: {i..j-},
lelt: i ≤ j < k,
ge: i ≥ j ,
decidable: Dec(P),
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
l_member: (x ∈ l),
nat: ℕ,
sq_type: SQType(T),
guard: {T},
last: last(L),
sorted-by: sorted-by(R;L),
less_than: a < b,
squash: ↓T
Latex:
\mforall{}[es:EO]. \mforall{}[s:fset(E)]. \mforall{}[i:Id].
s(i) \mmember{} \{e:E| (loc(e) = i) \mwedge{} e \mmember{} s \mwedge{} (\mforall{}e':E. (e' \mmember{} s {}\mRightarrow{} (\mneg{}(e <loc e'))))\} supposing i \mmember{} locs(s)
Date html generated:
2016_05_16-AM-10_14_47
Last ObjectModification:
2016_01_17-PM-01_21_33
Theory : new!event-ordering
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