Nuprl Lemma : list-eo-causl
∀L:Top List. ∀i:Id. ∀a,b:ℕ||L||. ((a < b) ⇐⇒ a < b)
Proof
Definitions occuring in Statement :
list-eo: list-eo(L;i),
es-causl: (e < e'),
Id: Id,
length: ||as||,
list: T List,
int_seg: {i..j-},
less_than: a < b,
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
natural_number: $n
Definitions unfolded in proof :
list-eo: list-eo(L;i),
es-causl: (e < e'),
mk-extended-eo: mk-extended-eo,
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
mk-eo: mk-eo(E;dom;l;R;locless;pred;rank),
mk-eo-record: mk-eo-record(E;dom;l;R;locless;pred;rank),
btrue: tt,
infix_ap: x f y,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
squash: ↓T,
prop: ℙ,
uall: ∀[x:A]. B[x],
int_seg: {i..j-},
rev_implies: P ⇐ Q
Latex:
\mforall{}L:Top List. \mforall{}i:Id. \mforall{}a,b:\mBbbN{}||L||. ((a < b) \mLeftarrow{}{}\mRightarrow{} a < b)
Date html generated:
2016_05_17-AM-08_22_20
Last ObjectModification:
2016_01_17-PM-02_34_54
Theory : event-ordering
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