Nuprl Lemma : State1-exists
∀[Info,A,B:Type]. ∀[init:B]. ∀[tr:Id ⟶ A ⟶ B ⟶ B]. ∀[X:EClass(A)].
∀es:EO+(Info). ∀e:E. (↓∃v:B. v ∈ State1(λloc.init;tr;X)(e))
Proof
Definitions occuring in Statement :
State1: State1(init;tr;X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
State1: State1(init;tr;X),
subtype_rel: A ⊆r B,
top: Top,
implies: P ⇒ Q,
not: ¬A,
false: False,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bag-null: bag-null(bs),
null: null(as),
single-bag: {x},
cons: [a / b],
bfalse: ff,
prop: ℙ,
squash: ↓T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[init:B]. \mforall{}[tr:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[X:EClass(A)].
\mforall{}es:EO+(Info). \mforall{}e:E. (\mdownarrow{}\mexists{}v:B. v \mmember{} State1(\mlambda{}loc.init;tr;X)(e))
Date html generated:
2016_05_17-AM-10_04_16
Last ObjectModification:
2016_01_17-PM-11_03_07
Theory : classrel!lemmas
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