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Proof step 8 from proof addarray-lastrec (previous step)

∀ r, val, i, st. addarray(r, vals + val ', i, st) = (addarray(r, vals, i, st)[r -- (n→i(# vals) + i) ', val]) ⊦ addarray(r, (val0 + vals) + val ', i, st) = (addarray(r, val0 + vals, i, st)[r -- (n→i(# (val0 + vals)) + i) ', val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ addarray(r, val ' + vals, i, st) = (addarray(r, vals, i + 1, st)[r -- i ', val])
Proof step 7:
∀ r, val, i, st. addarray(r, vals + val ', i, st) = (addarray(r, vals, i, st)[r -- (n→i(# vals) + i) ', val]) ⊦ (addarray(r, vals + val ', i + 1, st)[r -- i ', val0]) = (addarray(r, vals, i + 1, st)[r -- i ', val0][r -- ((1 + n→i(# vals)) + i) ', val])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ # val ' = 0 +1], [CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ val + vals = val ' + vals])]]