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Proof step 30 from proof RSA-decrypt-ij-vars (previous step)

((i - 1) * (i0 - 1)) * i1 + 1 < 1, 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 insert equation

And closed the goal!

Rule argument

pos: left 2 flags: rotate, discard

Additional information

Used simplifier rules: lsone: ⊦ i < 1 ↔ i ≤ 0; from specification int-abs%zero-le: ⊦ 0 < i → (i * j ≤ 0 ↔ j ≤ 0); from specification int-mult%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult