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Proof step 7 from proof mapped-full-last (previous step)

m + n < # avol, n ≤ n0 ∧ ¬ n + m < n0 ∧ n0 < # avol → avol[n0].mapped? ∧ # avol[n0].data = LEB_SIZE, ∀ n0. n ≤ n0 ∧ ¬ n + m < n0 ∧ n0 < # avol → avol[m + n, mapped(buf)][n0].mapped? ∧ # avol[m + n, mapped(buf)][n0].data = LEB_SIZE ⊦ n0 = m + n, # buf = LEB_SIZE ∧ (n ≤ n0 ∧ n0 < n + m ∧ n0 < # avol → avol[n0].mapped? ∧ # avol[n0].data = LEB_SIZE)

User applied rule all left

And closed the goal!

Rule argument

pos: left 3 terms: n + m abort: F discard: F computed: T

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ ¬ n < n; (s)% ⊦ m < # avol → avol[m, aleb][m] = aleb; (s)% ⊦ mapped(buf).mapped?; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ m < n → ¬ n < m; (s) Used terms: n + m