Nuprl Lemma : loop-class-state-total
∀[Info,B:Type]. ∀[init:Id ⟶ bag(B)]. ∀[X:EClass(B ⟶ B)]. ∀[es:EO+(Info)].
es-total-class(es;loop-class-state(X;init)) supposing ∀l:Id. (1 ≤ #(init l))
Proof
Definitions occuring in Statement :
loop-class-state: loop-class-state(X;init),
es-total-class: es-total-class(es;X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
bag-size: #(bs),
bag: bag(T)
Definitions unfolded in proof :
es-total-class: es-total-class(es;X),
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
and: P ∧ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
uiff: uiff(P;Q),
classrel: v ∈ X(e),
class-ap: X(e),
eclass: EClass(A[eo; e]),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
less_than: a < b,
squash: ↓T,
so_lambda: λ2x.t[x],
so_apply: x[s]
Latex:
\mforall{}[Info,B:Type]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[X:EClass(B {}\mrightarrow{} B)]. \mforall{}[es:EO+(Info)].
es-total-class(es;loop-class-state(X;init)) supposing \mforall{}l:Id. (1 \mleq{} \#(init l))
Date html generated:
2016_05_16-PM-11_35_48
Last ObjectModification:
2016_01_17-PM-07_05_42
Theory : event-ordering
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