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Proof step 7 from proof putArray-put-switch (previous step)

∀ i, j, r, st, val. i + n→i(# vals0) ≤ j ∧ 0 ≤ j ∧ 0 ≤ i → putArray(vals0, r, i, st[r -- j ', val]) = (putArray(vals0, r, i, st)[r -- j ', val]), i + n→i(# (val0 + vals0)) ≤ j, 0 ≤ j, 0 ≤ i ⊦ putArray(val0 + vals0, r, i, st[r -- j ', val]) = (putArray(val0 + vals0, r, i, st)[r -- j ', val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ putArray(val ' + vals, r, i, st) = (putArray(vals, r, i + 1, st)[r -- i ', val])
Proof step 6:
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 : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + 1 ≤ j ↔ i < j], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ # val ' = 0 +1], [CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ val + vals = val ' + vals])]]