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Proof step 4 from proof lookup-init-01 (previous step)

∀ r0, j, st, r, fs. (addarray(r0, vals0, j, st)[r -- fs ']) = st[r -- fs '] ⊦ (addarray(r0, val + vals0, j, st)[r -- fs ']) = st[r -- fs ']

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ addarray(r, val ' + vals, i, st) = (addarray(r, vals, i + 1, st)[r -- i ', val])
Proof step 3:
∀ r0, j, st, r, fs. (addarray(r0, vals0, j, st)[r -- fs ']) = st[r -- fs '] ⊦ (addarray(r0, vals0, j + 1, st)[r -- fs ']) = st[r -- fs ']

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ fs ' ≠ i '], [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])]]