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Proof step 32 from proof sis-pos-high (previous step)

# int2bits(j0) = 17, 0 < i0, j0 < 65536, 32767 < i0 * 65536 + j0, 32767 < j0, 0 ≤ j0, 0 ≤ i0, 0 < i0 * 65536 + j0, 0 < j0 ⊦ 16 = # fillsgn(17, int2bits(j0)).rest, j0 = s2i(i2s(bits2int(lastn(16, int2bits(i0) + fillsgn(17, int2bits(j0)).rest)))) + 65536

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
⊦ bits ≠ [] → # bits.rest = (# bits)-1
Proof step 34:
fillsgn(17, int2bits(j0)) ≠ [], # int2bits(j0) = 17, 0 < i0, j0 < 65536, 32767 < i0 * 65536 + j0, 32767 < j0, 0 ≤ j0, 0 ≤ i0, 0 < i0 * 65536 + j0, 0 < j0 ⊦ 16 = (# fillsgn(17, int2bits(j0)))-1, j0 = s2i(i2s(bits2int(lastn(16, int2bits(i0) + fillsgn(17, int2bits(j0)).rest)))) + 65536

Rule argument

spec: list-data inst: bitlista name: length-rest seq: ⊦ bits ≠ [] → # bits.rest = (# bits)-1 subst: [bits] → [fillsgn(17, int2bits(j0))] flags: rewrite

Additional information

Used simplifier rules: fill-empty: ⊦ fillsgn(n, bits) = [] ↔ bits = [] ∧ n = 0; from specification bitopsaux%int2bits-not-empty: ⊦ int2bits(j) ≠ []; from specification int2bits Used terms: fillsgn(17, int2bits(j0))