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Proof step 25 from proof sis-pos-low (previous step)

16 = # fillsgn(17, int2bits(j)).rest, 0 < i0, 0 ≤ i0, 0 ≤ j, 0 < 65536 * i0 + j, j ≤ 32767, 32767 < 65536 * i0 + j ⊦ s2i(i2s(bits2int(fillsgn(17, int2bits(j)).rest))) = j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ bits ≠ [] ∧ # bits < n → fillsgn(n, bits) = bits.first ' + fillsgn(n -1, bits)
Proof step 27:
¬(int2bits(j) ≠ [] ∧ # int2bits(j) < 17), 16 = # fillsgn(17, int2bits(j)).rest, 0 < i0, 0 ≤ i0, 0 ≤ j, 0 < 65536 * i0 + j, j ≤ 32767, 32767 < 65536 * i0 + j ⊦ s2i(i2s(bits2int(fillsgn(17, int2bits(j)).rest))) = j
Proof step 30:
int2bits(j) ≠ [] ∧ # int2bits(j) < 17, 16 = # (int2bits(j).first ' + fillsgn(17 -1, int2bits(j))).rest, 0 < i0, 0 ≤ i0, 0 ≤ j, 0 < 65536 * i0 + j, j ≤ 32767, 32767 < 65536 * i0 + j ⊦ s2i(i2s(bits2int((int2bits(j).first ' + fillsgn(17 -1, int2bits(j))).rest))) = j

Rule argument

seq: ⊦ bits ≠ [] ∧ # bits < n → fillsgn(n, bits) = bits.first ' + fillsgn(n -1, bits) subst: [bits, n] → [int2bits(j), 17] rotate: F spec: bitopsaux inst: name: fill-rec

Additional information

Used terms: int2bits(j), 17