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Proof step 26 from proof gcd-rec-sub-03 (previous step)

0 < i0 - abs(i) ∧ i0 - abs(i) < abs(i0), abs(i) < i0, i < 0 ⊦ i0 < 0, gcd(abs(i), i0 - abs(i)) = gcd(abs(i0), abs(i0) - (i0 - abs(i))), 0 < i ∧ i < i0 + i

User applied rule cut formula

And obtained the following new goals

Proof step 27:
abs(i0) - (i0 - abs(i)) = abs(i), 0 < i0 - abs(i) ∧ i0 - abs(i) < abs(i0), abs(i) < i0, i < 0 ⊦ i0 < 0, gcd(abs(i), i0 - abs(i)) = gcd(abs(i0), abs(i0) - (i0 - abs(i))), 0 < i ∧ i < i0 + i

Rule argument

fma: abs(i0) - (i0 - abs(i)) = abs(i)

Additional information

Used simplifier rules: Abs-pos: ⊦ ¬ j < 0 → abs(j) = j; from specification int-abs%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs%subneg: ⊦ i - ~ j = i + j; from specification int-abs%sub-add-09: ⊦ i - j + i = ~ j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%neg-12: ⊦ ~ i = ~ j ↔ i = j; from specification int-abs Used formulas: abs(i0) - (i0 - abs(i)) = abs(i)