Nuprl Lemma : iseg-global-order-history
∀[Info:Type]
∀L1,L2:(Id × Info) List. (L1 ≤ L2 ⇒ (∀e:E. (map(λx.info(x);≤loc(e)) = map(λx.info(x);≤loc(e)) ∈ Info List+)))
Proof
Definitions occuring in Statement :
global-eo: global-eo(L),
es-info: info(e),
es-le-before: ≤loc(e),
es-E: E,
Id: Id,
iseg: l1 ≤ l2,
listp: A List+,
map: map(f;as),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
lambda: λx.A[x],
product: x:A × B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
top: Top,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
less_than: a < b,
Id: Id,
sq_type: SQType(T),
guard: {T},
squash: ↓T,
true: True,
listp: A List+,
iseg: l1 ≤ l2,
sq_stable: SqStable(P),
l_exists: (∃x∈L. P[x]),
int_iseg: {i...j},
cand: A c∧ B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
nat: ℕ,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[Info:Type]
\mforall{}L1,L2:(Id \mtimes{} Info) List. (L1 \mleq{} L2 {}\mRightarrow{} (\mforall{}e:E. (map(\mlambda{}x.info(x);\mleq{}loc(e)) = map(\mlambda{}x.info(x);\mleq{}loc(e)))))
Date html generated:
2016_05_17-AM-08_33_08
Last ObjectModification:
2016_01_17-PM-02_30_12
Theory : event-ordering
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