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Proof step 37 from proof int2int-neg (previous step)

2 * 2 ^ i < 4 * 2 ^ i + j ∧ 4 * 2 ^ i + j < 3 * 2 ^ i, j ≤ 4 * 2 ^ i, j < 4 * 2 ^ i, j < 3 * 2 ^ i, j ≤ 3 * 2 ^ i, 2 ^ i + j ≤ 0, 0 < 2 ^ i * 2 + j, 2 ^ i + j ≤ i + 2, 2 ^ i + j < i + 2, j < i + 2, j < 0, j < 2 ^ i, j + 1 < 2 ^ i, j ≤ i, 0 ≤ i, j + 1 < 4 * 2 ^ i, 0 ≤ 4 * 2 ^ i + j, 0 < 4 * 2 ^ i + j, 2 ^ i + j ≤ i, j < i, j ≤ i + 2, j ≤ 0, j ≤ 2 ^ i, 0 ≤ 2 ^ i, 0 < 2 ^ i ⊦ 4 * 2 ^ i = 2 ^ (n→i(# uint2bits(4 * 2 ^ i + j)) - 1), 3 * 2 ^ i + j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 38:
2 * 2 ^ i ≤ j, j < 3 * 2 ^ i, 0 ≤ i ⊦ # uint2bits(j) = i→n(i + 3)
Proof step 39:
2 * 2 ^ i ≤ 4 * 2 ^ i + j ∧ 4 * 2 ^ i + j < 3 * 2 ^ i ∧ 0 ≤ i, 2 * 2 ^ i < 4 * 2 ^ i + j ∧ 4 * 2 ^ i + j < 3 * 2 ^ i, j ≤ 4 * 2 ^ i, j < 4 * 2 ^ i, j < 3 * 2 ^ i, j ≤ 3 * 2 ^ i, 2 ^ i + j ≤ 0, 0 < 2 ^ i * 2 + j, 2 ^ i + j ≤ i + 2, 2 ^ i + j < i + 2, j < i + 2, j < 0, j < 2 ^ i, j + 1 < 2 ^ i, j ≤ i, 0 ≤ i, j + 1 < 4 * 2 ^ i, 0 ≤ 4 * 2 ^ i + j, 0 < 4 * 2 ^ i + j, 2 ^ i + j ≤ i, j < i, j ≤ i + 2, j ≤ 0, j ≤ 2 ^ i, 0 ≤ 2 ^ i, 0 < 2 ^ i ⊦ 4 * 2 ^ i = 2 ^ (n→i(i→n(i + 3)) - 1), 3 * 2 ^ i + j = 0

Rule argument

name: uint2bits-len-01 rotate: F subst: [i, j] → [i, 4 * 2 ^ i + j]

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ (* i2) * i < (* i1) * i + j0 ↔ (i2 - i1) * i < j0;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ (* i2) * i + j < (* i1) * i ↔ j < (i1 - i2) * i;% ⊦ i * ~1 = ~ i;% ⊦ i < ~ j ↔ i + j < 0;% ⊦ (* i2) * i ≤ (* i1) * i + j0 ↔ (i2 - i1) * i ≤ j0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i < j ∧ i = i0 → i0 < j; (forward)% ⊦ i < j ∧ j = i0 → i < i0; (forward)% ⊦ i < j ∧ j < i0 → i +1 < i0; (forward)% ⊦ i < j ∧ j < j0 → i < j0; (forward)% ⊦ (* i) < j ∧ 0 < i → 0 ≤ j ∧ 0 < j; (forward)% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ 0 ≤ i ∧ i ≤ 1 → i = 0 ∨ i = 1; (forward) Used terms: i, 4 * 2 ^ i + j