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Proof step 11 from proof add-in-02 (previous step)

∀ r, r0, class1, st. r ∈ addobj(r0, class1, fis0, st) ↔ r = r0 ∨ r ∈ st ⊦ r ∈ addobj(r0, class1, fv ' + fis0, st) ↔ r = r0 ∨ r ∈ st

User applied rule structural induction

And obtained the following new goals

Proof step 10:
⊦ (∀ r, r0, class1, st. r ∈ addobj(r0, class1, fis0, st) ↔ r = r0 ∨ r ∈ st) → (r ∈ addobj(r0, class1, (sk × val) ' + fis0, st) ↔ r = r0 ∨ r ∈ st)

Rule argument

[VARWITHFMAVARSARG : fv, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : fieldvalue generated by ×;])]]