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Proof step 28 from proof int2int-neg (previous step)

2 ^ i + j ≤ n→i(# uint2bits(~ j)), 2 ^ i + j < n→i(# uint2bits(~ j)), j < n→i(# uint2bits(~ j)), j ≤ 0, j < 0, j < 2 ^ i, j + 1 < 2 ^ i, j + 1 < n→i(# uint2bits(~ j)), 0 < 2 ^ i * 2 + j, 0 ≤ i, 2 ^ i + j ≤ 0, j + 1 < 2 ^ n→i(# uint2bits(~ j)), 0 ≤ 2 ^ n→i(# uint2bits(~ j)) + j, 0 < 2 ^ n→i(# uint2bits(~ j)) + j, 2 ^ i + j ≤ i, 0 < 2 ^ i, j < i, j ≤ i, j ≤ 2 ^ n→i(# uint2bits(~ j)), 0 ≤ 2 ^ n→i(# uint2bits(~ j)), j < 2 ^ n→i(# uint2bits(~ j)), 0 < 2 ^ n→i(# uint2bits(~ j)), 1 < 2 ^ n→i(# uint2bits(~ j)), 2 ^ i + j ≤ 2 ^ n→i(# uint2bits(~ j)), i ≤ n→i(# uint2bits(~ j)), 2 ^ i + j < 2 ^ n→i(# uint2bits(~ j)), i < n→i(# uint2bits(~ j)), j ≤ n→i(# uint2bits(~ j)) ⊦ 2 ^ n→i(# uint2bits(~ j)) = 2 ^ (n→i(# uint2bits(2 ^ n→i(# uint2bits(~ j)) + j)) - 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
0 ≤ i, 2 ^ i ≤ j, j < 2 ^ (i + 1) ⊦ # uint2bits(j) = i→n(i + 2)
Proof step 30:
0 ≤ i ∧ 2 ^ i ≤ ~ j ∧ ~ j < 2 ^ (i + 1), 2 ^ i + j ≤ n→i(i→n(i + 2)), 2 ^ i + j < n→i(i→n(i + 2)), j < n→i(i→n(i + 2)), j ≤ 0, j < 0, j < 2 ^ i, j + 1 < 2 ^ i, j + 1 < n→i(i→n(i + 2)), 0 < 2 ^ i * 2 + j, 0 ≤ i, 2 ^ i + j ≤ 0, j + 1 < 2 ^ n→i(i→n(i + 2)), 0 ≤ 2 ^ n→i(i→n(i + 2)) + j, 0 < 2 ^ n→i(i→n(i + 2)) + j, 2 ^ i + j ≤ i, 0 < 2 ^ i, j < i, j ≤ i, j ≤ 2 ^ n→i(i→n(i + 2)), 0 ≤ 2 ^ n→i(i→n(i + 2)), j < 2 ^ n→i(i→n(i + 2)), 0 < 2 ^ n→i(i→n(i + 2)), 1 < 2 ^ n→i(i→n(i + 2)), 2 ^ i + j ≤ 2 ^ n→i(i→n(i + 2)), i ≤ n→i(i→n(i + 2)), 2 ^ i + j < 2 ^ n→i(i→n(i + 2)), i < n→i(i→n(i + 2)), j ≤ n→i(i→n(i + 2)) ⊦ 2 ^ n→i(i→n(i + 2)) = 2 ^ (n→i(# uint2bits(2 ^ n→i(i→n(i + 2)) + j)) - 1)

Rule argument

name: uint2bits-len rotate: F subst: [i, j] → [i, ~ j]

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i ≤ ~ j ↔ i + j ≤ 0;% ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j;% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ i * j = j * i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: i, ~ j