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Proof step 4 from proof putArray-put-switch-02 (previous step)

is_fskey(sk) ∨ r0 ≠ r, ¬ is_indexkey(sk) ∨ r0 ≠ r → putArray(vals0, r, i + 1, st[r0 -- sk, val]) = (putArray(vals0, r, i + 1, st)[r0 -- sk, val]), r0 ≠ r ∨ sk ≠ i ' ⊦ (putArray(vals0, r, i + 1, st[r0 -- sk, val])[r -- i ', val0]) = (putArray(vals0, r, i + 1, st)[r0 -- sk, val][r -- i ', val0])

User applied rule case distinction

And closed the goal!

Rule argument

[CASEDARG : pos: left 2, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)], [CSIMPSEQ : ⊦ i + j = j + i])]]