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Proof step 11 from proof band-011x-is-unsigned-03 (previous step)

2 ^ n→i(# int2bits(j) - 1) < abs(j) ⊦ band(j, 2 ^ n→i(# int2bits(j)) - 1) = bits2uint(int2bits(j))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ 0 < i ∧ 0 ≤ j → (2 ^ j < i ↔ i→n(j) + 2 ≤ # int2bits(i) ∧ i ≠ 2 ^ j)
Proof step 13:
0 < abs(j) ∧ 0 ≤ n→i(# int2bits(j) - 1), i→n(n→i(# int2bits(j) - 1)) + 2 ≤ # int2bits(abs(j)) ∧ abs(j) ≠ 2 ^ n→i(# int2bits(j) - 1) ⊦ band(j, 2 ^ n→i(# int2bits(j)) - 1) = bits2uint(int2bits(j))

Rule argument

seq: ⊦ 0 < i ∧ 0 ≤ j → (2 ^ j < i ↔ i→n(j) + 2 ≤ # int2bits(i) ∧ i ≠ 2 ^ j) subst: [i, j] → [abs(j), n→i(# int2bits(j) - 1)] rotate: F spec: int2bits inst: name: int2bits-lslen-12

Additional information

Used simplifier rules: band-num: ⊦ band((* i), (* j)) = bits2int(bitsand(int2bits(i), int2bits(j)));%band-associativity: ⊦ band(i, band(i0, j)) = band(band(i, i0), j);%band-commutativity: ⊦ band(i, j) = band(j, i);% ⊦ 0 < abs(i) ↔ i ≠ 0;% ⊦ 0 ≤ n→i(n);% ⊦ int2bits(0) = false ';% ⊦ # boolvar ' = 0 +1;% ⊦ bits2uint(false ') = 0; Used terms: abs(j), n→i(# int2bits(j) - 1)