Step
*
of Lemma
loop-class-memory-program_wf
∀[Info,B:Type].
∀[X:EClass(B ─→ B)]. ∀[init:Id ─→ bag(B)]. ∀[pr:LocalClass(X)].
(loop-class-memory-program(pr;init) ∈ LocalClass(loop-class-memory(X;init)))
supposing valueall-type(B)
BY
{ (Auto
THEN D (-1)
THEN Unfold `loop-class-memory-program` 0
THEN MemTypeCD
THEN Auto
THEN Reduce 0
THEN Assert ⌈hdf-memory(pr loc(e);init loc(e))*(map(λx.info(x);before(e)))
= hdf-memory(pr loc(e)*(map(λx.info(x);before(e)));loop-class-memory(X;init)(e))
∈ hdataflow(Info;B)⌉⋅) }
1
.....assertion.....
1. Info : Type
2. B : Type
3. valueall-type(B)
4. X : EClass(B ─→ B)
5. init : Id ─→ bag(B)
6. pr : Id ─→ hdataflow(Info;B ─→ B)
7. ∀es:EO+(Info). ∀e:E. (X(e) = (snd(pr loc(e)*(map(λx.info(x);before(e)))(info(e)))) ∈ bag(B ─→ B))
8. es : EO+(Info)@i'
9. e : E@i
⊢ hdf-memory(pr loc(e);init loc(e))*(map(λx.info(x);before(e)))
= hdf-memory(pr loc(e)*(map(λx.info(x);before(e)));loop-class-memory(X;init)(e))
∈ hdataflow(Info;B)
2
1. Info : Type
2. B : Type
3. valueall-type(B)
4. X : EClass(B ─→ B)
5. init : Id ─→ bag(B)
6. pr : Id ─→ hdataflow(Info;B ─→ B)
7. ∀es:EO+(Info). ∀e:E. (X(e) = (snd(pr loc(e)*(map(λx.info(x);before(e)))(info(e)))) ∈ bag(B ─→ B))
8. es : EO+(Info)@i'
9. e : E@i
10. hdf-memory(pr loc(e);init loc(e))*(map(λx.info(x);before(e)))
= hdf-memory(pr loc(e)*(map(λx.info(x);before(e)));loop-class-memory(X;init)(e))
∈ hdataflow(Info;B)
⊢ loop-class-memory(X;init)(e) = (snd(hdf-memory(pr loc(e);init loc(e))*(map(λx.info(x);before(e)))(info(e)))) ∈ bag(B)
Latex:
Latex:
\mforall{}[Info,B:Type].
\mforall{}[X:EClass(B {}\mrightarrow{} B)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[pr:LocalClass(X)].
(loop-class-memory-program(pr;init) \mmember{} LocalClass(loop-class-memory(X;init)))
supposing valueall-type(B)
By
Latex:
(Auto
THEN D (-1)
THEN Unfold `loop-class-memory-program` 0
THEN MemTypeCD
THEN Auto
THEN Reduce 0
THEN Assert \mkleeneopen{}hdf-memory(pr loc(e);init loc(e))*(map(\mlambda{}x.info(x);before(e)))
= hdf-memory(pr loc(e)*(map(\mlambda{}x.info(x);before(e)));loop-class-memory(X;init)(e))\mkleeneclose{}\mcdot{})
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