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

∀ class, st, r, i, val. addclass(class, fis0, st[r -- i ', val]) = (addclass(class, fis0, st)[r -- i ', val]) ⊦ (addclass(class0, fis0, st[r -- i ', val])[jvmref -- mkfs(class0, ty, fieldvar) ', val0]) = (addclass(class0, fis0, st)[jvmref -- mkfs(class0, ty, fieldvar) ', val0][r -- i ', 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 -- i ' ≠ jvmref -- mkfs(class0, ty, fieldvar) ', ∀ class, st, r, i, val. addclass(class, fis0, st[r -- i ', val]) = (addclass(class, fis0, st)[r -- i ', val]) ⊦ (addclass(class0, fis0, st[r -- i ', val])[jvmref -- mkfs(class0, ty, fieldvar) ', val0]) = (addclass(class0, fis0, st)[r -- i ', val][jvmref -- mkfs(class0, 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 -- i ', val0, jvmref -- mkfs(class0, ty, fieldvar) ', addclass(class0, fis0, st)] ,F ,store ,javastore ,rew ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ fs ' ≠ i '])], [EXTRATERMS : (val, r -- i ', val0, jvmref -- mkfs(class0, ty, fieldvar) ', addclass(class0, fis0, st))]]