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Proof step 7 from proof putar-rew (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
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])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + 1 ≤ j ↔ i < j])]]