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Proof step 22 from proof uint2bits-add-low-01 (previous step)

i→n(i) < # int2bits(j0), 0 < j, 1 < j, 0 ≤ i, 0 ≤ 2 ^ i + j0, 0 ≤ j0 + 2 ^ (i - 1), 0 < i, j0 < 0 ⊦ fillsgn(i→n(i) + 1, false ' + fillsgn(i→n(i), int2bits(j0))).rest = fillsgn(i→n(i), int2bits(j0)), j = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: int2bits-lslen-05 rotate: F subst: [i, m] → [j0, i→n(i)]

Additional information

Used simplifier rules: int2bits-neg-num: i < 0 ⊦ int2bits((* i)) = sgn(bitsinvert(uint2bits(abs(i))) +1);%uint2bits-one: ⊦ uint2bits(1) = false + true;% ⊦ 0 < i → n→i(i→n(i)) = i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < 0 → (~1 ≤ i ↔ i = ~1);% ⊦ boolvar + boolvar0 = boolvar ' + boolvar0 ';% ⊦ bitsinvert(false ' + bits) = true + bitsinvert(bits);% ⊦ bitsinvert(true ') = false ';% ⊦ boolvar + bits = boolvar ' + bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ (bits + false ')+1 = bits + true;% ⊦ bits + boolvar = bits + boolvar ';% ⊦ sgn(true ' + true ') = true ';% ⊦ 0 < i → fillsgn(i→n(i), boolvar ') = mklist(boolvar, i→n(i));%i < 0 ⊦ (* i) + j = j - ~ i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ # boolvar ' = 0 +1;%0 ≤ i ⊦ i→n(i) < (* m) ↔ i < n→i(m);% ⊦ 0 ≤ i → (i < 1 ↔ i = 0);% ⊦ mklist(boolvar, 0) = [];% ⊦ bits + [] = bits;% ⊦ fillsgn(1, boolvar ') = boolvar ';% ⊦ boolvar '.rest = []; Used terms: j0, i→n(i)