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

∀ i, j, r, st, r0. i < j ∨ n→i(# vals0) + j ≤ i → (putArray(vals0, r, j, st)[r0 -- i ']) = st[r0 -- i '] ⊦ i < j ∨ n→i(# (val + vals0)) + j ≤ i → (putArray(val + vals0, r, j, st)[r0 -- i ']) = st[r0 -- i ']

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

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [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 : ⊦ i ' = i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ val + vals = val ' + vals])]]