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Proof step 20 from proof band-011x-is-unsigned (previous step)

i→n(i) < # int2bits(~1), 0 ≤ i, 0 < i ⊦ 2 ^ i = (bits2int(fillsgn(i→n(i), int2bits(~1))) + 2 ^ n→i(# fillsgn(i→n(i), int2bits(~1)))) + 1, fillsgn(i→n(i), int2bits(~1)) = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i + 1 = 0 → int2bits(i) = true ' subst: [i] → [~1] rotate: F spec: int2bits inst: name: int2bits-mone

Additional information

Used simplifier rules: ⊦ 0 < i → fillsgn(i→n(i), boolvar ') = mklist(boolvar, i→n(i));% ⊦ # mklist(boolvar, n) = n;% ⊦ 0 < i → n→i(i→n(i)) = i;% ⊦ i = i + j ↔ j = 0;% ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ # boolvar ' = 0 +1;% ⊦ i ≠ j → (i ≤ j ↔ i < j);%0 ≤ i ⊦ i→n(i) < (* m) ↔ i < n→i(m);% ⊦ 0 ≤ i → (i < 1 ↔ i = 0); Used terms: ~1