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Proof step 27 from proof ac-bad (previous step)

∀ class1, class2, ty, fieldvar, val, fis1, st. class1 = class2 ∨ addclass(class1, fis0 + (mkfs(class2, ty, fieldvar) ' × val) ' + fis1, st) = addclass(class1, fis0 + fis1, st) ⊦ class1 = class2, addclass(class1, (fv ' + fis0) + (mkfs(class2, ty, fieldvar) ' × val) ' + fis1, st) = addclass(class1, (fv ' + fis0) + fis1, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ is_indexkey(fv .1) → addclass(class, fv ' + fis, st) = addclass(class, fis, st)
Proof step 21:
¬ is_indexkey(fv .1), ∀ class1, class2, ty, fieldvar, val, fis1, st. class1 = class2 ∨ addclass(class1, fis0 + (mkfs(class2, ty, fieldvar) ' × val) ' + fis1, st) = addclass(class1, fis0 + fis1, st) ⊦ class1 = class2, addclass(class1, (fv ' + fis0) + (mkfs(class2, ty, fieldvar) ' × val) ' + fis1, st) = addclass(class1, (fv ' + fis0) + fis1, st)
Proof step 26:
is_indexkey(fv .1), ∀ class1, class2, ty, fieldvar, val, fis1, st. class1 = class2 ∨ addclass(class1, fis0 + (mkfs(class2, ty, fieldvar) ' × val) ' + fis1, st) = addclass(class1, fis0 + fis1, st) ⊦ class1 = class2, addclass(class1, fis0 + (mkfs(class2, ty, fieldvar) ' × val) ' + fis1, st) = addclass(class1, (fv ' + fis0) + fis1, st)

Rule argument

[crewrite-arg: ac-no2 , F , [st, fis, fv, class] → [st, fis0 + (mkfs(class2, ty, fieldvar) ' × val) ' + fis1, fv, class1] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1])], [EXTRATERMS : (st, fis0 + (mkfs(class2, ty, fieldvar) ' × val) ' + fis1, fv, class1)]]