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Proof step 12 from proof modex-odd-neg (previous step)

2 * j = (i0 * 2 + j0) + 1, j0 < 2, j ≤ 0, 0 ≤ i0, 0 ≤ j0 ⊦ j0 = ~1

User applied rule cut formula

And closed the goal!

Rule argument

fma: j0 = 1

Additional information

Used simplifier rules: ⊦ i ≠ 1 ∧ 0 ≤ i → (i < 2 ↔ i = 0); (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ abs(j1) < abs(i) ∧ j1 ≠ 0 → i * j ≠ i * j0 + j1; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i * j + i = i * (j + 1); (s)% ⊦ 0 < i → (i * j = i * j0 ↔ j = j0); (s)% ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j; (s)% ⊦ i ≤ ~1 ↔ i < 0; (s)% ⊦ i ≤ j → (j < i ↔ false); (as) Used formulas: j0 = 1