Nuprl Lemma : alle-between2-false
∀es:EO. ∀e1:E. ∀e2:{e:E| loc(e) = loc(e1) ∈ Id} . (∀e∈[e1,e2].False ⇐⇒ (e2 <loc e1))
Proof
Definitions occuring in Statement :
alle-between2: ∀e∈[e1,e2].P[e],
es-locl: (e <loc e'),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
false: False,
set: {x:A| B[x]} ,
equal: s = t ∈ T
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],
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
rev_implies: P ⇐ Q,
decidable: Dec(P),
or: P ∨ Q,
alle-between2: ∀e∈[e1,e2].P[e],
false: False,
guard: {T}
Latex:
\mforall{}es:EO. \mforall{}e1:E. \mforall{}e2:\{e:E| loc(e) = loc(e1)\} . (\mforall{}e\mmember{}[e1,e2].False \mLeftarrow{}{}\mRightarrow{} (e2 <loc e1))
Date html generated:
2016_05_16-AM-09_44_41
Last ObjectModification:
2015_12_28-PM-09_39_19
Theory : new!event-ordering
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