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Proof step 7 from proof enc-invert (previous step)

⊦ ( ((maxenc(m) - (m - (maxenc(m) * (maxenc(m) + 1)) / 2)) + (m - (maxenc(m) * (maxenc(m) + 1)) / 2)) * ((maxenc(m) - (m - (maxenc(m) * (maxenc(m) + 1)) / 2)) + (m - (maxenc(m) * (maxenc(m) + 1)) / 2) + 1)) / 2 + (m - (maxenc(m) * (maxenc(m) + 1)) / 2) = m

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 8:
⊦ m % n = 0 ∧ n ≠ 0 → (∃ n0. m = n * n0)
Proof step 9:
(maxenc(m) * (maxenc(m) + 1)) % 2 = 0 ∧ 2 ≠ 0 → (∃ n0. maxenc(m) * (maxenc(m) + 1) = 2 * n0) ⊦ ( ((maxenc(m) - (m - (maxenc(m) * (maxenc(m) + 1)) / 2)) + (m - (maxenc(m) * (maxenc(m) + 1)) / 2)) * ((maxenc(m) - (m - (maxenc(m) * (maxenc(m) + 1)) / 2)) + (m - (maxenc(m) * (maxenc(m) + 1)) / 2) + 1)) / 2 + (m - (maxenc(m) * (maxenc(m) + 1)) / 2) = m

Rule argument

spec: nat-div inst: name: exmult seq: ⊦ m % n = 0 ∧ n ≠ 0 → (∃ n0. m = n * n0) subst: [m, n] → [maxenc(m) * (maxenc(m) + 1), 2] flags:

Additional information

Used terms: maxenc(m) * (maxenc(m) + 1), 2