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Proof step 6 from proof putar-rew (previous step)

n→i(# vals0) + j < sk .index ∨ r0 ≠ r ∨ is_fskey(sk) ∨ sk .index < j, r0 ≠ r ∨ sk ≠ j ', ¬ j < sk .index ∨ ¬ is_indexkey(sk) ∨ r0 ≠ r ∨ ¬ sk .index ≤ n→i(# vals0) + j → (putArray(vals0, r, j + 1, st)[r0 -- sk, val0]) = putArray(vals0, r, j + 1, st[r0 -- sk, val0]) ⊦ (putArray(vals0, r, j + 1, st)[r0 -- sk, val0][r -- j ', val]) = (putArray(vals0, r, j + 1, st[r0 -- sk, val0])[r -- j ', val])

User applied rule case distinction

And obtained the following new goals

Proof step 5:
n→i(# vals0) + j < sk .index ∨ r0 ≠ r ∨ is_fskey(sk) ∨ sk .index < j, r0 ≠ r ∨ sk ≠ j ' ⊦ ¬ j < sk .index ∨ ¬ is_indexkey(sk) ∨ r0 ≠ r ∨ ¬ sk .index ≤ n→i(# vals0) + j, (putArray(vals0, r, j + 1, st)[r0 -- sk, val0][r -- j ', val]) = (putArray(vals0, r, j + 1, st[r0 -- sk, val0])[r -- j ', val])

Rule argument

[CASEDARG : pos: left 3, ()]

Additional information

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