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Proof step 39 from proof cast-mod-pos-low (previous step)

i→n(i) = # fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, 2 ^ i ≤ j, 0 ≤ 2 ^ (i - 1) + j, j % 2 ^ i < j, 2 ^ (i - 1) ≤ j, 0 ≤ j, 0 < i, j % 2 ^ i < 2 ^ (i - 1) ⊦ bits2int(fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest) = j % 2 ^ i

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ bits ≠ [] ∧ # bits < n → fillsgn(n, bits) = bits.first ' + fillsgn(n -1, bits) subst: [bits, n] → [int2bits(j % 2 ^ i), i→n(i) + 1] rotate: F spec: bitopsaux inst: name: fill-rec

Additional information

Used simplifier rules: ⊦ int2bits(j).first ↔ j < 0;% ⊦ (m + 1)-1 = m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ (boolvar ' + bits).rest = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ bits ≠ [] → bits2int(fillsgn(n, bits)) = bits2int(bits);% ⊦ bits2int(int2bits(i)) = i;% ⊦ int2bits(j) ≠ []; Used terms: int2bits(j % 2 ^ i), i→n(i) + 1