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Proof step 14 from proof cong-mult-rew (previous step)

⊦ j | i * (j * i3 + i2) - i1 ↔ j | i * i2 - i1

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: i * (j * i3 + i2) - i1 = j * i * i3 + (i * i2 - i1)

Additional information

Used simplifier rules: sub-add-01: ⊦ i + (j - i0) = i + j - i0; 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%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs%Sub-def: ⊦ i + (j - i) = j; from specification int-abs%eq-dist: ⊦ (i + j) * i0 = j0 + j * i0 ↔ i * i0 = j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult Used formulas: i * (j * i3 + i2) - i1 = j * i * i3 + (i * i2 - i1)