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Proof step 22 from proof enc-invert (previous step)

maxenc(m) * (maxenc(m) + 1) = 2 * n0, 2 * m < (maxenc(m) + 1) * (maxenc(m) + 2), maxenc(m) * (maxenc(m) + 1) ≤ 2 * m ⊦ m < n0, m - n0 ≤ maxenc(m)

User applied rule insert lemma

And obtained the following new goals

Proof step 23:
⊦ (maxenc(m) * (maxenc(m) + 1)) / 2 ≤ m ∧ m < ((maxenc(m) + 1) * (maxenc(m) + 2)) / 2
Proof step 24:
maxenc(m) * (maxenc(m) + 1) = 2 * n0, 2 * m < (maxenc(m) + 1) * (maxenc(m) + 2), m < ((maxenc(m) + 1) * (maxenc(m) + 2)) / 2, maxenc(m) * (maxenc(m) + 1) ≤ 2 * m, (maxenc(m) * (maxenc(m) + 1)) / 2 ≤ m ⊦ m < n0, m - n0 ≤ maxenc(m)

Rule argument

spec: <toplevel> name: max-size seq: ⊦ (maxenc(m) * (maxenc(m) + 1)) / 2 ≤ m ∧ m < ((maxenc(m) + 1) * (maxenc(m) + 2)) / 2 subst: [m] → [m]

Additional information

Used terms: m