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Proof step 23 from proof band-011x-is-unsigned-fix (previous step)

# int2bits(j) < i→n(i), 0 < i, 2 ^ n→i(1 + i→n(i) - 2) < abs(j) ⊦ 1 + i→n(i) - 2 = i→n(i) - 1, band(j, 2 ^ i - 1) = bits2uint(fillsgn(i→n(i), int2bits(j))), i = 0

User applied rule insert elim lemma

And closed the goal!

Rule argument

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

Additional information

Used simplifier rules: ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ m + 1 ≠ 0;% ⊦ (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: i→n(i), m