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Proof step 29 from proof sis-neg-low (previous step)

16 ≤ # int2bits(j0).rest, # int2bits(j0) = 17, j0 < 0, j0 < ~32768, i0 * 65536 + j0 < ~32768, ~65536 < j0, i0 * 65536 + j0 < 0, i0 < 0 ⊦ j0 = 0, s2i(i2s(bits2int(lastn(16, int2bits(i0 - 1) + int2bits(j0).rest)))) = j0 + 65536

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
# int2bits(j0) = 17, i0 < 0, i0 * 65536 + j0 < 0, ~65536 < j0, i0 * 65536 + j0 < ~32768, j0 < ~32768, j0 < 0, 16 ≤ # int2bits(j0).rest ⊦ s2i(i2s(bits2int(lastn(16, int2bits(j0).rest)))) = j0 + 65536, j0 = 0, int2bits(j0).rest = []

Rule argument

Additional information

Used simplifier rules: l: ⊦ # bits = 0 ↔ bits = []; from specification list-data[bitlista]%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%a: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; from specification list[bitlista]%lastN-append-01: ⊦ n ≤ # bits → lastn(n, bits0 + bits) = lastn(n, bits); from specification list-del[bitlista]