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Proof step 11 from proof ac-shift-02 (previous step)

∀ class1, st, ty, fieldvar, val. (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val]) = addclass(class1, fis0[mkfs(class1, ty, fieldvar) ', val], st) ⊦ (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty0, fieldvar0) ', val0][jvmref -- mkfs(class1, ty, fieldvar) ', val]) = addclass(class1, ((mkfs(class1, ty0, fieldvar0) ' × val0) ' + fis0)[mkfs(class1, ty, fieldvar) ', val], st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val])
Proof step 7:
⊦ addclass(class1, (mkfs(class1, ty, fieldvar) ' × val) ' + fis, st) = (addclass(class1, fis, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val])
Proof step 10:
jvmref -- mkfs(class1, ty, fieldvar) ' ≠ jvmref -- mkfs(class1, ty0, fieldvar0) ', ∀ class1, st, ty, fieldvar, val. (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val]) = addclass(class1, fis0[mkfs(class1, ty, fieldvar) ', val], st) ⊦ (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val][jvmref -- mkfs(class1, ty0, fieldvar0) ', val0]) = addclass(class1, ((mkfs(class1, ty0, fieldvar0) ' × val0) ' + fis0)[mkfs(class1, ty, fieldvar) ', val], st)

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val]) ,[val0, rk, val, rk0, st] → [val, jvmref -- mkfs(class1, ty, fieldvar) ', val0, jvmref -- mkfs(class1, ty0, fieldvar0) ', addclass(class1, fis0, st)] ,F ,store ,javastore ,rew ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ fs ' = fs0 ' ↔ fs = fs0], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) = mkfs(class0, ty0, fieldvar0) ↔ class = class0 ∧ ty = ty0 ∧ fieldvar = fieldvar0], [CSIMPSEQ : ⊦ (st[rk, val][rk, val0]) = st[rk, val0]], [CSIMPSEQ : ⊦ ((sk × val) ' + fis)[sk, val0] = (sk × val0) ' + fis], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1])], [EXTRATERMS : (val, jvmref -- mkfs(class1, ty, fieldvar) ', val0, jvmref -- mkfs(class1, ty0, fieldvar0) ', addclass(class1, fis0, st))]]