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Proof step 12 from proof ac-shift-03 (previous step)

∀ class, st, ty, fieldvar, val. (addclass(class, fis0, st)[jvmref -- mkfs(class, ty, fieldvar) ', val]) = addclass(class, fis0[mkfs(class, ty, fieldvar) ', val], st), ty ≠ ty0 ∨ fieldvar ≠ fieldvar0 ⊦ (addclass(class0, fis0, st)[jvmref -- mkfs(class0, ty0, fieldvar0) ', val0][jvmref -- mkfs(class0, ty, fieldvar) ', val]) = (addclass(class0, fis0[mkfs(class0, ty, fieldvar) ', val], st)[jvmref -- mkfs(class0, ty0, fieldvar0) ', val0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val])
Proof step 11:
jvmref -- mkfs(class0, ty, fieldvar) ' ≠ jvmref -- mkfs(class0, ty0, fieldvar0) ', ∀ class, st, ty, fieldvar, val. (addclass(class, fis0, st)[jvmref -- mkfs(class, ty, fieldvar) ', val]) = addclass(class, fis0[mkfs(class, ty, fieldvar) ', val], st), ty ≠ ty0 ∨ fieldvar ≠ fieldvar0 ⊦ (addclass(class0, fis0, st)[jvmref -- mkfs(class0, ty, fieldvar) ', val][jvmref -- mkfs(class0, ty0, fieldvar0) ', val0]) = (addclass(class0, fis0[mkfs(class0, ty, fieldvar) ', val], st)[jvmref -- mkfs(class0, ty0, fieldvar0) ', val0])

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val]) ,[val0, rk, val, rk0, st] → [val, jvmref -- mkfs(class0, ty, fieldvar) ', val0, jvmref -- mkfs(class0, ty0, fieldvar0) ', addclass(class0, 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])], [EXTRATERMS : (val, jvmref -- mkfs(class0, ty, fieldvar) ', val0, jvmref -- mkfs(class0, ty0, fieldvar0) ', addclass(class0, fis0, st))]]