Nuprl Lemma : es-before-pred-length
∀[es:EO]. ∀[e:E]. ||before(e)|| = (||before(pred(e))|| + 1) ∈ ℤ supposing ¬↑first(e)
Proof
Definitions occuring in Statement :
es-before: before(e),
es-first: first(e),
es-pred: pred(e),
es-E: E,
event_ordering: EO,
length: ||as||,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
add: n + m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
es-before: before(e),
le: A ≤ B,
less_than': less_than'(a;b),
uiff: uiff(P;Q),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff
Latex:
\mforall{}[es:EO]. \mforall{}[e:E]. ||before(e)|| = (||before(pred(e))|| + 1) supposing \mneg{}\muparrow{}first(e)
Date html generated:
2016_05_16-AM-09_37_43
Last ObjectModification:
2016_01_17-PM-01_27_52
Theory : new!event-ordering
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