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Proof step 35 from proof int2int-lastn-negpos (previous step)

bits2int(bits) * 2 ^ n→i(m) + bits2int(lastn(m, int2bits(i))) = i, int2bits(i) = bits + lastn(m, int2bits(i)), # bits = # int2bits(i) - m, 1 + m < # sgn(lastn(m, int2bits(i))), bits2int(bits) + 1 < bits2int(lastn(m, int2bits(i))), i + 1 < bits2int(lastn(m, int2bits(i))), 0 < bits2int(lastn(m, int2bits(i))), bits2int(bits) + 1 < 2 ^ n→i(m), bits2int(bits) < bits2int(lastn(m, int2bits(i))), i < 2 ^ n→i(m), i + 1 < 2 ^ n→i(m), i < bits2int(lastn(m, int2bits(i))), i < 0, 0 < 2 ^ n→i(m), 0 ≤ bits2int(lastn(m, int2bits(i))), m ≤ # int2bits(i), bits2int(bits) < 0, bits2int(bits) < 2 ^ n→i(m) ⊦ bits2int(lastn(m, int2bits(i))) % 2 ^ n→i(m) = 0, bits = [], m = 0, i % 2 ^ n→i(m) = 0, bits2int(lastn(m, int2bits(i))) = bits2int(lastn(m, int2bits(i))) % 2 ^ n→i(m)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ # bits ≤ n → ¬ n < # sgn(bits) subst: [bits, n] → [lastn(m, int2bits(i)), 1 + m] rotate: F spec: bitopsaux inst: name: sgn-nls

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ n ≤ # bits → # lastn(n, bits) = n;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ ¬ m + n < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: lastn(m, int2bits(i)), 1 + m