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Proof step 21 from proof band-011x-is-unsigned-03 (previous step)

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

User applied rule insert elim lemma

And closed the goal!

Rule argument

seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [# int2bits(j), m] rotate: T spec: nat inst: name: elim-pred-c

Additional information

Used simplifier rules: ⊦ # bits = 0 ↔ bits = [];% ⊦ int2bits(j) ≠ [];% ⊦ n→i(m + n) = n→i(m) + n→i(n);% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ n ≤ m → m + n0 - n = (m - n) + n0;% ⊦ 0 + m = m;%n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: # int2bits(j), m