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Proof step 89 from proof cast-mod-neg-low (previous step)

i→n(i) = # int2bits(j % 2 ^ i) - 1, 2 ^ i + j % 2 ^ i < 0, j % 2 ^ i < 0, j + 2 ^ i < i, j + 2 ^ i ≤ 0, 2 ^ (i - 1) + j < 0, j < 2 ^ (i - 1), j % 2 ^ i + 2 ^ (i - 1) < 0, j < 0, 0 < i, i→n(i) < # int2bits(j % 2 ^ i), j % 2 ^ i < ~1 ⊦ 2 ^ (n→i(# int2bits(j % 2 ^ i)) - 1) = 2 ^ i, j = ~1, i = 1, j % 2 ^ i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 90:
n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1

Rule argument

seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [# int2bits(j % 2 ^ i), i→n(i)] rotate: F spec: nat inst: name: elim-pred-c

Additional information

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