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Proof step 19 from proof div2-nls-02 (previous step)

i + j = i0 * 2 + 1, i0 < i, i0 < j, 0 < i, 0 < j, i ≤ j, 0 ≤ i + j, 0 ≤ i0 ⊦

User applied rule cut formula

And closed the goal!

Rule argument

fma: i = i0 * 2 + 1 - j

Additional information

Used simplifier rules: ⊦ i - j = i0 ↔ i = i0 + j; (s)% ⊦ i + (j - i) = j; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i + j = i + i0 ↔ j = i0; (s)% ⊦ i < j - i0 ↔ i + i0 < j; (s)% ⊦ i + j < (* i1) * i + j0 ↔ j < (i1 - 1) * i + j0; (s)% ⊦ 1 * i = i; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i < j + 1 ↔ i ≤ j; (s)% ⊦ i < j → (j ≤ i ↔ false); (as) Used formulas: i = i0 * 2 + 1 - j