Nuprl Lemma : es-interval-length-one-one
∀[es:EO]. ∀[d,b,a:E]. (b = d ∈ E) supposing ((||[a, b]|| = ||[a, d]|| ∈ ℤ) and a ≤loc d and a ≤loc b )
Proof
Definitions occuring in Statement :
es-interval: [e, e'],
es-le: e ≤loc e' ,
es-E: E,
event_ordering: EO,
length: ||as||,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
or: P ∨ Q,
cand: A c∧ B,
true: True,
squash: ↓T,
subtype_rel: A ⊆r B,
top: Top,
ge: i ≥ j ,
decidable: Dec(P),
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
rev_implies: P ⇐ Q
Latex:
\mforall{}[es:EO]. \mforall{}[d,b,a:E]. (b = d) supposing ((||[a, b]|| = ||[a, d]||) and a \mleq{}loc d and a \mleq{}loc b )
Date html generated:
2016_05_16-AM-09_33_26
Last ObjectModification:
2016_01_17-PM-01_30_05
Theory : new!event-ordering
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