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Proof step 19 from proof addarray-mklist-05 (conclusion)

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

User applied rule structural induction

And obtained the following new goals

Proof step 5:
⊦ addarray(r, ty, mklist(initial_value(ty), 0), st) = (addarray(r, initial_value(ty), n→i(0), st)[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(0))])
Proof step 18:
∀ 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

[VARWITHVARSEQSARG : n, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : nat generated by 0, +1;])]]