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Proof step 12 from proof addarray-mklist-05 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ n ≠ 0 → mklist(val, n) = mklist(val, n -1) + val '
Proof step 11:
m + 1 ≠ 0, 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) -1) + initial_value(ty) ') .butlast, st) [r -- n→i(m) ', (mklist(initial_value(ty), (m + 1) -1) + initial_value(ty) ') .last ] [r -- _length, intval(n→i(m) + 1) ] ) = (addarray(r, initial_value(ty), n→i(m), st)[r -- n→i(m) ', initial_value(ty)][r -- _type, typeval(mkarraytype(ty))] [r -- _length, intval(n→i(m) + 1) ] )

Rule argument

[speclemmaarg: ,n ≠ 0 → mklist(val, n) = mklist(val, n -1) + val ' ,[n, val] → [m + 1, initial_value(ty)] ,F ,list-last ,javavalues ,mk-last-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + 1 ≠ 0], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (m + 1, initial_value(ty))]]