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Proof step 7 from proof init-switch (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 6:
is_fskey(sk) ⊦ ¬ is_indexkey(sk), sk = i ', (addarray(r, vals0, i + 1, st[r -- sk, val0])[r -- i ', val]) = (addarray(r, vals0, i + 1, st)[r -- sk, val0][r -- i ', val])

Rule argument

[CASEDARG : pos: left 2, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i])]]