Nuprl Lemma : l_before-es-before-iff
∀the_es:EO. ∀e,e',y:E. (e' before y ∈ before(e) ⇐⇒ (e' <loc y) ∧ (y <loc e))
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],
iff: P ⇐⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
not: ¬A,
uimplies: b supposing a,
false: False,
es-before: before(e),
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
guard: {T},
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
or: P ∨ Q,
cand: A c∧ B,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B
Latex:
\mforall{}the$_{es}$:EO. \mforall{}e,e',y:E. (e' before y \mmember{} before(e) \mLeftarrow{}{}\mRightarrow{} (e' <loc y) \mwedge{} (y <loc e\000C))
Date html generated:
2016_05_16-AM-09_30_19
Last ObjectModification:
2016_01_17-PM-01_31_01
Theory : new!event-ordering
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