Nuprl Lemma : es-pred-one-one
∀[es:EO]. ∀[a,b:E]. (a = b ∈ E) supposing ((pred(a) = pred(b) ∈ E) and (¬↑first(b)) and (¬↑first(a)))
Proof
Definitions occuring in Statement :
es-first: first(e),
es-pred: pred(e),
es-E: E,
event_ordering: EO,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
equal: s = t ∈ T
Lemmas :
pes-axioms,
Id_wf,
es-loc_wf,
iff_weakening_equal,
es-le-pred,
es-le_wf,
equal_wf,
es-E_wf,
es-pred_wf,
not_wf,
assert_wf,
es-first_wf2,
event_ordering_wf,
es-locl_irreflexivity,
es-loc-pred,
and_wf
\mforall{}[es:EO]. \mforall{}[a,b:E]. (a = b) supposing ((pred(a) = pred(b)) and (\mneg{}\muparrow{}first(b)) and (\mneg{}\muparrow{}first(a)))
Date html generated:
2015_07_17-AM-08_39_18
Last ObjectModification:
2015_02_04-AM-07_07_51
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