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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
and: P ∧ Q,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
guard: {T},
rev_implies: P ⇐ Q,
or: P ∨ Q,
prop: ℙ,
false: False
Latex:
\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:
2016_05_16-AM-09_23_47
Last ObjectModification:
2015_12_28-PM-09_51_21
Theory : new!event-ordering
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