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Proof step 5 from proof shift-1init-01 (previous step)

r0 -- sk ≠ r -- j ', ∀ r, r0, j, st, sk, val. r = r0 ∨ (addarray(r, vals0, j, st)[r0 -- sk, val]) = addarray(r, vals0, j, st[r0 -- sk, val]) ⊦ r = r0, (addarray(r, vals0, j + 1, st)[r0 -- sk, val][r -- j ', val0]) = (addarray(r, vals0, j + 1, st[r0 -- sk, val])[r -- j ', val0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
∀ r, r0, j, st, sk, val. r = r0 ∨ (addarray(r, vals0, j, st)[r0 -- sk, val]) = addarray(r, vals0, j, st[r0 -- sk, val]) ⊦ r = r0, (addarray(r, vals0, j + 1, st)[r0 -- sk, val][r -- j ', val0]) = (addarray(r, vals0, j + 1, st[r0 -- sk, val])[r -- j ', val0])

Rule argument

[emptyarg]

Additional information

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