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Proof step 42 from proof bor-2pot-plus-01 (previous step)

# int2bits(j0) = i→n(i) + 1, # int2bits(j0).rest < i→n(i), 0 < i, j0 < 2 ^ i, j < 2 ^ i, (¬ mklist(false, i→n(i)).first) ∈ bitsinvert(uint2bits(~ j)) +1, j + 1 < 2 ^ i, j < j0, j < i, 0 < 2 ^ i, 0 ≤ j0, j + 1 < i, j < 0 ⊦ bitsinvert(int2bits(j)) + mklist(true, i→n(i)) = [], i = 0, bits2int(int2bits(j) + bitsinvert(bitsand(bitsinvert(int2bits(j0).rest), mklist(true, i→n(i))))) = j * 2 ^ i + j0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ bits ≠ [] → # bits.rest = (# bits)-1 subst: [bits] → [int2bits(j0)] rotate: F spec: list-data inst: bitlista name: length-rest

Additional information

Used simplifier rules: ⊦ n -1 = n - 1;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < 1 ↔ m = 0;% ⊦ # bits = 0 ↔ bits = [];%n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m < n + 1 ↔ ¬ n < m;%⊦ 0 ≤ j ∧ j < 2 ^ i → (i→n(i) < # int2bits(j) ↔ # int2bits(j) = i→n(i) + 1);% ⊦ int2bits(j) ≠ []; Used terms: int2bits(j0)