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Proof step 5 from proof putArray-put-switch (previous step)

0 ≤ j, 0 ≤ i, n→i(# vals0) + i < j, ¬ j < (i + 1) + n→i(# vals0) ∧ ¬ j < 0 ∧ ¬ i + 1 < 0 → putArray(vals0, r, i + 1, st[r -- j ', val]) = (putArray(vals0, r, i + 1, st)[r -- j ', val]), ∀ i0, j0, r0, st0, val1. ¬ j0 < i0 + n→i(# vals0) ∧ ¬ j0 < 0 ∧ ¬ i0 < 0 → putArray(vals0, r0, i0, st0[r0 -- j0 ', val1]) = (putArray(vals0, r0, i0, st0)[r0 -- j0 ', val1]) ⊦ (putArray(vals0, r, i + 1, st[r -- j ', val])[r -- i ', val0]) = (putArray(vals0, r, i + 1, st)[r -- i ', val0][r -- j ', val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
putArray(vals0, r, i + 1, st[r -- j ', val]) = (putArray(vals0, r, i + 1, st)[r -- j ', val]), 0 ≤ j, 0 ≤ i, n→i(# vals0) + i < j, ∀ i0, j0, r0, st0, val1. ¬ j0 < i0 + n→i(# vals0) ∧ ¬ j0 < 0 ∧ ¬ i0 < 0 → putArray(vals0, r0, i0, st0[r0 -- j0 ', val1]) = (putArray(vals0, r0, i0, st0)[r0 -- j0 ', val1]) ⊦ (putArray(vals0, r, i + 1, st)[r -- j ', val][r -- i ', val0]) = (putArray(vals0, r, i + 1, st)[r -- i ', val0][r -- j ', val])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ 0 ≤ i ∧ 0 ≤ j → ¬ i + j < 0], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j])]]