Nuprl Lemma : l_before-es-before
∀the_es:EO. ∀e,e',y:E. (e' before y ∈ before(e) ⇒ (e' <loc y))
Proof
Definitions occuring in Statement :
es-before: before(e),
es-locl: (e <loc e'),
es-E: E,
event_ordering: EO,
l_before: x before y ∈ l,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
es-before: before(e),
all: ∀x:A. B[x],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
guard: {T},
false: False,
iff: P ⇐⇒ Q,
decidable: Dec(P),
or: P ∨ Q,
rev_implies: P ⇐ Q,
l_before: x before y ∈ l,
sublist: L1 ⊆ L2,
top: Top,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
squash: ↓T,
true: True,
int_seg: {i..j-},
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
nat: ℕ,
ge: i ≥ j ,
increasing: increasing(f;k),
subtract: n - m,
less_than: a < b,
select: L[n],
cons: [a / b],
l_member: (x ∈ l),
cand: A c∧ B
Latex:
\mforall{}the$_{es}$:EO. \mforall{}e,e',y:E. (e' before y \mmember{} before(e) {}\mRightarrow{} (e' <loc y))
Date html generated:
2016_05_16-AM-09_30_12
Last ObjectModification:
2016_01_17-PM-01_33_25
Theory : new!event-ordering
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