Nuprl Lemma : es-pplus-alle-between2
∀es:EO. ∀e1:E. ∀e2:{e:E| loc(e) = loc(e1) ∈ Id} .
∀[Q:{e:E| loc(e) = loc(e1) ∈ Id} ⟶ ℙ]. ([e1,e2]~([a,b].∀e∈[a,b].Q[e])+ ⇐⇒ e1 ≤loc e2 ∧ ∀e∈[e1,e2].Q[e])
Proof
Definitions occuring in Statement :
es-pplus: [e1,e2]~([a,b].p[a; b])+,
alle-between2: ∀e∈[e1,e2].P[e],
es-le: e ≤loc e' ,
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
iff: 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],
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
so_apply: x[s1;s2],
prop: ℙ,
rev_implies: P ⇐ Q,
es-pplus: [e1,e2]~([a,b].p[a; b])+,
es-pstar-q: [e1;e2]~([a,b].p[a; b])*[a,b].q[a; b],
exists: ∃x:A. B[x],
alle-between2: ∀e∈[e1,e2].P[e],
not: ¬A,
int_seg: {i..j-},
lelt: i ≤ j < k,
nat_plus: ℕ+,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
le: A ≤ B,
less_than: a < b,
subtype_rel: A ⊆r B,
uiff: uiff(P;Q),
subtract: n - m,
sq_type: SQType(T),
guard: {T},
upto: upto(n),
from-upto: [n, m),
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
bfalse: ff,
concat: concat(ll),
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
squash: ↓T,
true: True,
cand: A c∧ B,
es-locl: (e <loc e'),
less_than': less_than'(a;b),
nat: ℕ,
ge: i ≥ j ,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
bnot: ¬bb,
assert: ↑b
Latex:
\mforall{}es:EO. \mforall{}e1:E. \mforall{}e2:\{e:E| loc(e) = loc(e1)\} .
\mforall{}[Q:\{e:E| loc(e) = loc(e1)\} {}\mrightarrow{} \mBbbP{}]
([e1,e2]\msim{}([a,b].\mforall{}e\mmember{}[a,b].Q[e])+ \mLeftarrow{}{}\mRightarrow{} e1 \mleq{}loc e2 \mwedge{} \mforall{}e\mmember{}[e1,e2].Q[e])
Date html generated:
2016_05_16-AM-09_58_29
Last ObjectModification:
2016_01_17-PM-01_30_21
Theory : new!event-ordering
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