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Proof step 11 from proof addclass-switch-01 (previous step)

∀ r, class, st, sk, val. r = jvmref ∨ addclass(class, fis0, st[r -- sk, val]) = (addclass(class, fis0, st)[r -- sk, val]) ⊦ r = jvmref, (addclass(class, fis0, st[r -- sk, val])[jvmref -- mkfs(class, ty, fieldvar) ', val0]) = (addclass(class, fis0, st)[jvmref -- mkfs(class, ty, fieldvar) ', val0][r -- sk, val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val])
Proof step 10:
r -- sk ≠ jvmref -- mkfs(class, ty, fieldvar) ', ∀ r, class, st, sk, val. r = jvmref ∨ addclass(class, fis0, st[r -- sk, val]) = (addclass(class, fis0, st)[r -- sk, val]) ⊦ r = jvmref, (addclass(class, fis0, st[r -- sk, val])[jvmref -- mkfs(class, ty, fieldvar) ', val0]) = (addclass(class, fis0, st)[r -- sk, val][jvmref -- mkfs(class, ty, fieldvar) ', val0])

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0])], [EXTRATERMS : (val, r -- sk, val0, jvmref -- mkfs(class, ty, fieldvar) ', addclass(class, fis0, st))]]