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Proof step 16 from proof uint2bits-len-01 (previous step)

2 ≤ i1 * 2 + j1, i1 * 2 + j1 < 3, j1 < 2, 0 ≤ j1, 0 ≤ i1, 0 < i1 * 2 + j1, 0 < i1, ∀ j0, i. i→n(j0) < i→n(i1 * 2 + j1) → 0 ≤ i ∧ j0 < 3 * 2 ^ i ∧ 2 * 2 ^ i ≤ j0 ∧ 0 < 2 ^ i → # uint2bits(j0) = i→n(i + 3) ⊦ 2 = # uint2bits(i1), i1 * 2 + j1 = 1

User applied rule cut formula

And closed the goal!

Rule argument

fma: j1 = 1

Additional information

Used simplifier rules: uint2bits-one: ⊦ uint2bits(1) = false + true;% ⊦ 0 ≤ i → (i < 1 ↔ i = 0);% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ 2 * i = 0 ↔ i = 0;% ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0;% ⊦ i ≠ 1 ∧ 0 ≤ i → (i < 2 ↔ i = 0);% ⊦ i < j ∧ i = i0 → i0 < j; (forward)% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 2 * i ≠ 1;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ 0 < i ∧ 0 ≤ j → ((* i) * i0 < (* j) ↔ i0 < (i + j - 1) / i);% ⊦ 0 < j → (j < 2 ↔ j = 1);% ⊦ i = 1 → i * j = j;% ⊦ boolvar + boolvar0 = boolvar ' + boolvar0 ';% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used formulas: j1 = 1