Nuprl Lemma : last-transition
∀es:EO. ∀e:E. ∀P:{a:E| loc(a) = loc(e) ∈ Id} ⟶ 𝔹.
(∀e'≤e.P[e'] = P[e] ∨ ∃e'≤e.(¬P[e'] = P[e]) ∧ ∀e''∈(e',e].P[e''] = P[e])
Proof
Definitions occuring in Statement :
alle-between3: ∀e∈(e1,e2].P[e],
alle-le: ∀e≤e'.P[e],
existse-le: ∃e≤e'.P[e],
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
bool: 𝔹,
so_apply: x[s],
all: ∀x:A. B[x],
not: ¬A,
or: P ∨ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
prop: ℙ,
or: P ∨ Q,
and: P ∧ Q,
uimplies: b supposing a,
guard: {T},
alle-le: ∀e≤e'.P[e],
decidable: Dec(P),
not: ¬A,
false: False,
alle-between3: ∀e∈(e1,e2].P[e],
existse-le: ∃e≤e'.P[e],
exists: ∃x:A. B[x],
cand: A c∧ B,
es-locl: (e <loc e')
Latex:
\mforall{}es:EO. \mforall{}e:E. \mforall{}P:\{a:E| loc(a) = loc(e)\} {}\mrightarrow{} \mBbbB{}.
(\mforall{}e'\mleq{}e.P[e'] = P[e] \mvee{} \mexists{}e'\mleq{}e.(\mneg{}P[e'] = P[e]) \mwedge{} \mforall{}e''\mmember{}(e',e].P[e''] = P[e])
Date html generated:
2016_05_16-AM-09_50_58
Last ObjectModification:
2015_12_28-PM-09_36_22
Theory : new!event-ordering
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