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Proof step 54 from proof bor-2pot-plus-01 (previous step)

# int2bits(j0) = i→n(i) + 1, 2 + j < 2 ^ i, 1 < 2 ^ i, 0 < i, j0 < 2 ^ i, j < 2 ^ i, (¬ mklist(false, i→n(i)).first) ∈ bitsinvert(uint2bits(~ j)) +1, j < j0, j < i, 0 ≤ j0, j + 1 < i, j < 0, 0 < j0, j + 1 < j0, 0 < 2 ^ i, 0 ≤ 2 ^ i ⊦ bitsinvert(int2bits(j)) + mklist(true, i→n(i)) = [], i = 0, int2bits(j0).rest = [], 2 ^ i = 2 ^ (n→i(# uint2bits(j0)) - 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ i → int2bits(i) = uint2bits(i) subst: [i] → [j0] rotate: T spec: int2bits inst: name: int2bits-pos

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ n→i(m + n) = n→i(m) + n→i(n);% ⊦ 0 < i → n→i(i→n(i)) = i;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ (* i) + i0 - (* j) = (i - j) + i0;% ⊦ i + 0 = i; Used terms: j0