Nuprl Lemma : es-pred-exists-between
∀es:EO. ∀e1,e2:E. ((e1 <loc e2) ⇒ (∃e:{e:E| ¬↑first(e)} . (e1 = pred(e) ∈ E)))
Proof
Definitions occuring in Statement :
es-locl: (e <loc e'),
es-first: first(e),
es-pred: pred(e),
es-E: E,
event_ordering: EO,
assert: ↑b,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
set: {x:A| B[x]} ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
implies: P ⇒ Q,
guard: {T},
uall: ∀[x:A]. B[x],
nat: ℕ,
prop: ℙ,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
and: P ∧ Q,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
es-locl: (e <loc e'),
so_lambda: λ2x.t[x],
so_apply: x[s],
le: A ≤ B,
less_than': less_than'(a;b),
uiff: uiff(P;Q)
Latex:
\mforall{}es:EO. \mforall{}e1,e2:E. ((e1 <loc e2) {}\mRightarrow{} (\mexists{}e:\{e:E| \mneg{}\muparrow{}first(e)\} . (e1 = pred(e))))
Date html generated:
2016_05_16-AM-09_22_18
Last ObjectModification:
2016_01_17-PM-01_30_49
Theory : new!event-ordering
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