Nuprl Lemma : State-loc-comb-non-empty-iff
∀[Info,B,A:Type]. ∀[f:Id ⟶ A ⟶ B ⟶ B]. ∀[init:Id ⟶ bag(B)].
∀X:EClass(A). ∀es:EO+(Info). ∀e:E. (¬↑bag-null(init loc(e)) ⇐⇒ ↓∃v:B. v ∈ State-loc-comb(init;f;X)(e))
Proof
Definitions occuring in Statement :
State-loc-comb: State-loc-comb(init;f;X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
assert: ↑b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
squash: ↓T,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
bag-null: bag-null(bs),
bag: bag(T)
Definitions unfolded in proof :
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q,
squash: ↓T,
uiff: uiff(P;Q),
uimplies: b supposing a,
not: ¬A,
nat: ℕ,
gt: i > j,
nequal: a ≠ b ∈ T ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,B,A:Type]. \mforall{}[f:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[init:Id {}\mrightarrow{} bag(B)].
\mforall{}X:EClass(A). \mforall{}es:EO+(Info). \mforall{}e:E.
(\mneg{}\muparrow{}bag-null(init loc(e)) \mLeftarrow{}{}\mRightarrow{} \mdownarrow{}\mexists{}v:B. v \mmember{} State-loc-comb(init;f;X)(e))
Date html generated:
2016_05_17-AM-10_02_09
Last ObjectModification:
2016_01_17-PM-11_03_33
Theory : classrel!lemmas
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