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Proof step 17 from proof inv-flashsize-app (previous step)

# x0 = # lax0, # x1 = # lax1, (lax0 + lax1)[n] = @(m, m0), n < # lax0 + # lax1, ∀ n. n < # lax1 → lax1[n].size = x1[n].flashsize, ∀ n. n < # lax0 → lax0[n].size = x0[n].flashsize ⊦ m0 = x1[n - # x0].flashsize, n < # x0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
# x0 = # lax0, # x1 = # lax1, (lax0 + lax1)[n] = @(m, m0), n < # lax0 + # lax1, # lax0 ≤ n, ∀ n. n < # lax1 → lax1[n].size = x1[n].flashsize, ∀ n. n < # lax0 → lax0[n].size = x0[n].flashsize ⊦ lax1 = [], m0 = x1[n - # lax0].flashsize

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ # lax = 0 ↔ lax = []; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)