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Proof step 4 from proof length-1init (previous step)

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

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:
∀ r, j, st. (addarray(r, vals0, j, st)[r -- _length]) = st[r -- _length] ⊦ (addarray(r, vals0, j + 1, st)[r -- _length]) = st[r -- _length]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ _length ≠ 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])]]