Nuprl Lemma : integer-class-bound-exists
∀[Info:Type]. ∀es:EO+(Info). ∀X:EClass(ℤ). ∀e:E. ∃b:ℕ+. ∀x:ℤ. (x ∈ X(e) ⇒ x < b)
Proof
Definitions occuring in Statement :
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
nat_plus: ℕ+,
less_than: a < b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
nat_plus: ℕ+,
so_apply: x[s],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
nat: ℕ,
uimplies: b supposing a,
guard: {T},
le: A ≤ B,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
false: False,
uiff: uiff(P;Q),
subtract: n - m,
top: Top,
less_than': less_than'(a;b),
true: True,
cons-bag: x.b,
bag-size: #(bs),
eclass: EClass(A[eo; e]),
less_than: a < b,
squash: ↓T,
satisfiable_int_formula: satisfiable_int_formula(fmla),
rev_uimplies: rev_uimplies(P;Q),
sq_or: a ↓∨ b,
classrel: v ∈ X(e)
Latex:
\mforall{}[Info:Type]. \mforall{}es:EO+(Info). \mforall{}X:EClass(\mBbbZ{}). \mforall{}e:E. \mexists{}b:\mBbbN{}\msupplus{}. \mforall{}x:\mBbbZ{}. (x \mmember{} X(e) {}\mRightarrow{} x < b)
Date html generated:
2016_05_17-AM-06_43_08
Last ObjectModification:
2016_01_17-PM-06_34_26
Theory : event-ordering
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