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Proof step 18 from proof addarray-mklist-05 (previous step)

∀ r, ty, st. addarray(r, ty, mklist(initial_value(ty), m), st) = (addarray(r, initial_value(ty), n→i(m), st)[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(m))]) ⊦ addarray(r, ty, mklist(initial_value(ty), m +1), st) = (addarray(r, initial_value(ty), n→i(m +1), st)[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(m +1))])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
∀ r, ty, st. addarray(r, ty, mklist(initial_value(ty), m), st) = (addarray(r, initial_value(ty), n→i(m), st)[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(m))]) ⊦ addarray(r, ty, mklist(initial_value(ty), m + 1), st) = (addarray(r, initial_value(ty), n→i(m) + 1, st)[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(m) + 1)])

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 : ⊦ m +1 = m + 1])]]