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Proof step 10 from proof putAr-get-other-01 (previous step)

# vals0 + i→n(i) < i→n(j), 0 ≤ i, ∀ i0, j0, r0, st0, r2. ¬ i→n(j0) < i→n(i0) + # vals0 ∧ ¬ i0 < 0 → (putArray(vals0, r0, i0, st0)[r2 -- j0 ']) = st0[r2 -- j0 '] ⊦ r1 -- j ' = r -- i ', (putArray(vals0, r, i + 1, st)[r -- i ', val][r1 -- j ']) = st[r1 -- j '], j = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ r ≠ r0 → (putArray(vals, r, j, st)[r0 -- sk]) = st[r0 -- sk]
Proof step 9:
0 ≤ i, # vals0 + i→n(i) < i→n(j), ∀ i0, j0, r0, st0, r2. ¬ i→n(j0) < i→n(i0) + # vals0 ∧ ¬ i0 < 0 → (putArray(vals0, r0, i0, st0)[r2 -- j0 ']) = st0[r2 -- j0 '] ⊦ j = i, j = 0, (putArray(vals0, r, i + 1, st)[r -- i ', val][r -- j ']) = st[r -- j ']

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ ¬ m + n < m], [CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)], [CSIMPSEQ : ⊦ r ≠ r0 → (st[r0 -- sk0, val][r -- sk]) = st[r -- sk]], [CSIMPSEQ : ⊦ i ' = i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])]]