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Proof step 14 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) ⊦ (addclass(class0, fis0, st)[jvmref -- mkfs(class0, ty0, fieldvar0) ', val0][jvmref -- mkfs(class0, ty, fieldvar) ', val]) = addclass(class0, ((mkfs(class0, ty0, fieldvar0) ' × val0) ' + fis0)[mkfs(class0, ty, fieldvar) ', val], st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ sk ≠ sk0 → ((sk0 × val) ' + fis)[sk, val0] = (sk0 × val) ' + fis[sk, val0]
Proof step 7:
⊦ addclass(class1, (mkfs(class1, ty, fieldvar) ' × val) ' + fis, st) = (addclass(class1, fis, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val])
Proof step 13:
mkfs(class0, ty, fieldvar) ' ≠ 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) ⊦ (addclass(class0, fis0, st)[jvmref -- mkfs(class0, ty0, fieldvar0) ', val0][jvmref -- mkfs(class0, ty, fieldvar) ', val]) = addclass(class0, (mkfs(class0, ty0, fieldvar0) ' × val0) ' + fis0[mkfs(class0, ty, fieldvar) ', val], st)

Rule argument

[speclemmaarg: , sk ≠ sk0 → ((sk0 × val) ' + fis)[sk, val0] = (sk0 × val) ' + fis[sk, val0] ,[val0, sk, fis, val, sk0] → [val, mkfs(class0, ty, fieldvar) ', fis0, val0, mkfs(class0, ty0, fieldvar0) '] ,F ,assoclist ,fieldinit ,put-no ]

Additional information

[[CONCRETESIMPRULES : ([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, mkfs(class0, ty, fieldvar) ', fis0, val0, mkfs(class0, ty0, fieldvar0) ')]]