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Proof step 65 from proof bor-2pot-plus (previous step)

int2bits(j0) = false ' + bitsinvert(bits), 0 < j, j0 < 2 ^ i, 0 ≤ i, 0 ≤ j0, 0 < 2 ^ i, 0 ≤ j, false ∈ int2bits(j0), # int2bits(j0) ≤ i→n(i) ⊦ fillsgn(i→n(i), bitsinvert(int2bits(j0))) = [], bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = [], 2 ^ n→i(# fillsgn(i→n(i), bitsinvert(int2bits(j0)))) = 2 ^ i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 66:
⊦ # bits ≤ n → # fillsgn(n, bits) = n

Rule argument

seq: ⊦ # bits ≤ n → # fillsgn(n, bits) = n subst: [bits, n] → [bitsinvert(int2bits(j0)), i→n(i)] rotate: F spec: bitopsaux inst: name: fill-length

Additional information

Used simplifier rules: ⊦ 0 ≤ i → n→i(i→n(i)) = i;% ⊦ 0 ≤ i ∧ 0 ≤ j → (2 ^ i = 2 ^ j ↔ i = j);% ⊦ # bitsinvert(bits) = # bits;% ⊦ ¬ m ≤ n ↔ n < m;%⊦ 0 ≤ j ∧ j < 2 ^ i → (i→n(i) < # int2bits(j) ↔ # int2bits(j) = i→n(i) + 1);% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m = n + 1 → ¬ m ≤ n; Used terms: bitsinvert(int2bits(j0)), i→n(i)