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Proof step 9 from proof lpt-leb-size-write (previous step)

∀ n. n < # lpt → lpt[n].size ≤ LEB_SIZE ⊦ (∀ n0. n0 < # lpt → lpt[n, mklp(m, m0, lpf, m1)][n0].size ≤ LEB_SIZE) ↔ # lpt ≤ n ∨ m0 ≤ LEB_SIZE, # lpt ≤ n

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
n < # lpt, ∀ n. n < # lpt → lpt[n].size ≤ LEB_SIZE ⊦ (∀ n0. n0 < # lpt → lpt[n, mklp(m, m0, lpf, m1)][n0].size ≤ LEB_SIZE) ↔ m0 ≤ LEB_SIZE

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)