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Proof step 13 from proof cong-crt (previous step)

∃ i0. j0 * i0 = i - 1, prime(j), prime(j0), 0 < i, j | i - 1 ⊦ j = j0, j * j0 | i - 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
prime(j0), prime(j), j | j0 * i0, 0 ≤ j0 * i0 ⊦ j = j0, j * j0 | j0 * i0

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%mone-06: ⊦ ~1 < i ↔ 0 ≤ i; from specification int-abs%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%ax-04: ⊦ i + 0 = i; from specification int-basic2%numsub: ⊦ (* i) + i0 - (* j) = (i - j) + i0; from specification int-abs%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs