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Proof step 11 from proof addarray-mklist-05 (previous step)

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) ] )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
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, initial_value(ty), n→i(m), st)[r -- _type, typeval(mkarraytype(ty))][r -- n→i(m) ', initial_value(ty)] [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

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (st[rk, val][rk0, val0][rk, val1] ) = (st[rk0, val0][rk, val1])], [CSIMPSEQ : ⊦ m + 1 ≠ 0], [CSIMPSEQ : ⊦ (vals + val ') .last = val], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ (vals + val ') .butlast = vals], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ (m + 1) -1 = m])]]