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Proof step 27 from proof putAr-lastrec (previous step)

r -- (i + n→i(# (val0 ' + vals0))) ' ≠ r -- i ', ∀ val, r, i, st. putArray(vals0 + val ', r, i, st) = (putArray(vals0, r, i, st)[r -- (i + n→i(# vals0)) ', val]) ⊦ (putArray(vals0 + val ', r, i + 1, st)[r -- i ', val0]) = (putArray(vals0, r, i + 1, st)[r -- (i + n→i(# (val0 ' + vals0))) ', val][r -- i ', val0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 26:
∀ val, r, i, st. putArray(vals0 + val ', r, i, st) = (putArray(vals0, r, i, st)[r -- (i + n→i(# vals0)) ', val]) ⊦ (putArray(vals0 + val ', r, i + 1, st)[r -- i ', val0]) = (putArray(vals0, r, i + 1, st)[r -- ((1 + n→i(# vals0)) + i) ', val][r -- i ', val0])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ 0 ≠ n→i(m) + 1], [CSIMPSEQ : ⊦ i = i + j ↔ j = 0], [CSIMPSEQ : ⊦ i ' = i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ # val ' = 0 +1], [CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0])]]