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Proof step 13 from proof ac-del (previous step)

∀ class1, sk, val0, fis1, st, val. (addclass(class1, fis0 + (sk × val0) ' + fis1, st)[jvmref -- sk, val]) = (addclass(class1, fis0 + fis1, st)[jvmref -- sk, val]) ⊦ (addclass(class, fis0 + (sk × val0) ' + fis1, st)[jvmref -- mkfs(class, ty, fieldvar) ', val1][jvmref -- sk, val]) = (addclass(class, fis0 + fis1, st)[jvmref -- mkfs(class, ty, fieldvar) ', val1][jvmref -- sk, val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val])
Proof step 7:
¬ jvmref -- sk ≠ jvmref -- mkfs(class, ty, fieldvar) ', ∀ class1, sk, val0, fis1, st, val. (addclass(class1, fis0 + (sk × val0) ' + fis1, st)[jvmref -- sk, val]) = (addclass(class1, fis0 + fis1, st)[jvmref -- sk, val]) ⊦ (addclass(class, fis0 + (sk × val0) ' + fis1, st)[jvmref -- mkfs(class, ty, fieldvar) ', val1][jvmref -- sk, val]) = (addclass(class, fis0 + fis1, st)[jvmref -- mkfs(class, ty, fieldvar) ', val1][jvmref -- sk, val])
Proof step 12:
jvmref -- sk ≠ jvmref -- mkfs(class, ty, fieldvar) ', ∀ class1, sk, val0, fis1, st, val. (addclass(class1, fis0 + (sk × val0) ' + fis1, st)[jvmref -- sk, val]) = (addclass(class1, fis0 + fis1, st)[jvmref -- sk, val]) ⊦ (addclass(class, fis0 + (sk × val0) ' + fis1, st)[jvmref -- sk, val][jvmref -- mkfs(class, ty, fieldvar) ', val1]) = (addclass(class, fis0 + fis1, st)[jvmref -- mkfs(class, ty, fieldvar) ', val1][jvmref -- sk, val])

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val]) ,[val0, rk, val, rk0, st] → [val, jvmref -- sk, val1, jvmref -- mkfs(class, ty, fieldvar) ', addclass(class, fis0 + (sk × val0) ' + fis1, st)] ,F ,store ,javastore ,rew ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (val, jvmref -- sk, val1, jvmref -- mkfs(class, ty, fieldvar) ', addclass(class, fis0 + (sk × val0) ' + fis1, st))]]