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Proof step 19 from proof ac-lookup-02 (previous step)

is_fskey(fv .1), ∀ class1, class2, st, ty, fieldvar. class1 = class2 ∨ (addclass(class2, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = st[jvmref -- mkfs(class1, ty, fieldvar) '] ⊦ class1 = class2, (addclass(class2, fv ' + fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = st[jvmref -- mkfs(class1, ty, fieldvar) ']

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 18:
fv = sk × val, is_fskey(sk), ∀ class1, class2, st, ty, fieldvar. class1 = class2 ∨ (addclass(class2, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = st[jvmref -- mkfs(class1, ty, fieldvar) '] ⊦ class1 = class2, (addclass(class2, fv ' + fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = st[jvmref -- mkfs(class1, ty, fieldvar) ']

Rule argument

[speclemmaarg: ,sk = fv .1 ∧ val = fv .2 ↔ fv = sk × val ,[fv, sk, val] → [fv, sk, val] ,T ,pair ,fieldinit ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ sk = fv .1 ∧ val = fv .2 ↔ fv = sk × val])], [EXTRATERMS : (fv, sk, val)]]