Nuprl Lemma : implies-es-pred
∀[the_es:EO]. ∀[e,e':E]. e = pred(e') ∈ E supposing (e <loc e') ∧ (∀e1:E. (¬((e <loc e1) ∧ (e1 <loc e'))))
Proof
Definitions occuring in Statement :
es-locl: (e <loc e'),
es-pred: pred(e),
es-E: E,
event_ordering: EO,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
not: ¬A,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
false: False,
guard: {T},
rev_implies: P ⇐ Q,
or: P ∨ Q
Latex:
\mforall{}[the$_{es}$:EO]. \mforall{}[e,e':E].
e = pred(e') supposing (e <loc e') \mwedge{} (\mforall{}e1:E. (\mneg{}((e <loc e1) \mwedge{} (e1 <loc e'))))
Date html generated:
2016_05_16-AM-09_23_21
Last ObjectModification:
2015_12_28-PM-09_52_26
Theory : new!event-ordering
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