Step
*
of Lemma
Memory-classrel1
∀[Info,B,A:Type]. ∀[f:A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:B].
uiff(v ∈ Memory-class(f;init;X)(e);↓((↑first(e)) ∧ v ↓∈ init loc(e))
∨ ((¬↑first(e))
∧ ((∃a:A
(a ∈ X(pred(e))
∧ (∃b:B. (b ∈ Memory-class(f;init;X)(pred(e)) ∧ (v = (f a b) ∈ B)))))
∨ ((∀a:A. (¬a ∈ X(pred(e)))) ∧ v ∈ Memory-class(f;init;X)(pred(e))))))
BY
{ (UnivCD THENA MaAuto) }
1
1. Info : Type
2. B : Type
3. A : Type
4. f : A ─→ B ─→ B
5. init : Id ─→ bag(B)
6. X : EClass(A)
7. es : EO+(Info)
8. e : E
9. v : B
⊢ uiff(v ∈ Memory-class(f;init;X)(e);↓((↑first(e)) ∧ v ↓∈ init loc(e))
∨ ((¬↑first(e))
∧ ((∃a:A
(a ∈ X(pred(e))
∧ (∃b:B. (b ∈ Memory-class(f;init;X)(pred(e)) ∧ (v = (f a b) ∈ B)))))
∨ ((∀a:A. (¬a ∈ X(pred(e)))) ∧ v ∈ Memory-class(f;init;X)(pred(e))))))
Latex:
Latex:
\mforall{}[Info,B,A:Type]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[X:EClass(A)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
\mforall{}[v:B].
uiff(v \mmember{} Memory-class(f;init;X)(e);\mdownarrow{}((\muparrow{}first(e)) \mwedge{} v \mdownarrow{}\mmember{} init loc(e))
\mvee{} ((\mneg{}\muparrow{}first(e))
\mwedge{} ((\mexists{}a:A
(a \mmember{} X(pred(e))
\mwedge{} (\mexists{}b:B
(b \mmember{} Memory-class(f;init;X)(pred(e))
\mwedge{} (v = (f a b))))))
\mvee{} ((\mforall{}a:A. (\mneg{}a \mmember{} X(pred(e))))
\mwedge{} v \mmember{} Memory-class(f;init;X)(pred(e))))))
By
Latex:
(UnivCD THENA MaAuto)
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