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Proof step 7 from proof ac-lookup (previous step)

mkfs(class, ty, fieldvar) ' ∈ fis0, ∀ class1, ty, fieldvar, st. mkfs(class1, ty, fieldvar) ' ∈ fis0 → (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = fis0[mkfs(class1, ty, fieldvar) '] ⊦ (((ty = ty0 ∧ fieldvar = fieldvar0) ⊃ val; addclass(class, fis0, st)[jvmref -- mkfs(class, ty, fieldvar) '])) = ((mkfs(class, ty0, fieldvar0) ' × val) ' + fis0)[mkfs(class, ty, fieldvar) ']

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 6:
ty ≠ ty0 ∨ fieldvar ≠ fieldvar0, mkfs(class, ty, fieldvar) ' ∈ fis0, ∀ class1, ty, fieldvar, st. mkfs(class1, ty, fieldvar) ' ∈ fis0 → (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = fis0[mkfs(class1, ty, fieldvar) '] ⊦ (addclass(class, fis0, st)[jvmref -- mkfs(class, ty, fieldvar) ']) = ((mkfs(class, ty0, fieldvar0) ' × val) ' + fis0)[mkfs(class, ty, fieldvar) ']

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ((sk × val) ' + fis)[sk] = val], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1])]]