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Proof step 29 from proof RSA-decrypt-ij-vars (previous step)

i2 * i3 = ((i - 1) * (i0 - 1)) * i1 + 1, gcd(i2, (i - 1) * (i0 - 1)) = 1, ((i - 1) * (i0 - 1)) * i1 < i, ((i - 1) * (i0 - 1)) * i1 < i3, ((i - 1) * (i0 - 1)) * i1 < i0, ((i - 1) * (i0 - 1)) * i1 < j, ((i - 1) * (i0 - 1)) * i1 < 0, j < i * i0, 0 < i, 0 < i2, 1 < i * i0, 0 ≤ i2, 0 < i3, 0 < i0, 0 < j, prime(i), prime(i0), 2 < i, 2 < i0, i2 < i * i0, ((i - 1) * (i0 - 1)) * i1 < i * i0 ⊦ j = j ^ (i2 * i3) |%| (i * i0), i = i0, i3 = 0, j = 0

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: ((i - 1) * (i0 - 1)) * i1 + 1 < 1

Additional information

Used simplifier rules: numls-03: ⊦ i + (* j) < (* j0) ↔ i < j0 - j; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); 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 Used formulas: ((i - 1) * (i0 - 1)) * i1 + 1 < 1