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Proof step 9 from proof inv-write-buf (previous step)

avol[n, mapped(buf)][n0] = mapped(buf1), avol[n] = mapped(buf0), n0 < # avol, n < # avol, # buf0 ≤ LEB_SIZE → # buf ≤ LEB_SIZE, avol[n0].mapped? → # avol[n0].data ≤ LEB_SIZE ∧ (n0 ≠ n → is-aligned(# avol[n0].data, EB_PAGE_SIZE)) ⊦ # buf1 ≤ LEB_SIZE ∧ (n0 ≠ n → is-aligned(# avol[n0].data, EB_PAGE_SIZE))

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: n0 = n

Additional information

Used simplifier rules: ⊦ m ≠ n → avol[n, aleb][m] = avol[m]; (s)% ⊦ mapped(buf).mapped?; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ m < # avol → avol[m, aleb][m] = aleb; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ m < n → (n ≤ m ↔ false); (s) Used formulas: n0 = n