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Proof step 6 from proof shift-1dim-01 (previous step)

r0 -- sk ≠ r -- i1 ', 0 ≤ i1, ∀ val, sk, st, val0, r0, r, i0. i→n(i0) < i→n(i1 + 1) → (true → r = r0 ∨ (addarray(r, val0, i0, st)[r0 -- sk, val]) = addarray(r, val0, i0, st[r0 -- sk, val])) ⊦ r = r0, (addarray(r, val0, i1, st)[r0 -- sk, val][r -- i1 ', val0]) = (addarray(r, val0, i1, st[r0 -- sk, val])[r -- i1 ', val0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
0 ≤ i1, ∀ val, sk, st, val0, r0, r, i0. i→n(i0) < i→n(i1 + 1) → (true → r = r0 ∨ (addarray(r, val0, i0, st)[r0 -- sk, val]) = addarray(r, val0, i0, st[r0 -- sk, val])) ⊦ r = r0, (addarray(r, val0, i1, st)[r0 -- sk, val][r -- i1 ', val0]) = (addarray(r, val0, i1, st[r0 -- sk, val])[r -- i1 ', val0])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])]]