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Proof step 18 from proof inv-write-buf (previous step)

# lpt = # avol, avol[n0] = mapped(buf0), m = buffered(n0).leb, buffered(n0).isbuf?, avol[m].mapped?, m < # avol, n0 < # avol, n1 < n, awbuf-inv(avol, buffered(n0)), is-aligned(# avol[m].data + n1, EB_PAGE_SIZE), 0 + n1 ≤ # buf, # buf0 + n ≤ LEB_SIZE, n ≤ # buf, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪isbuf := true⟫ ( awbuf-inv(avol[m, mapped(avol[m].data + subarray(buf, 0, n1))], buffered(n0)) ∧ # lpt = # avol[m, mapped(avol[m].data + subarray(buf, 0, n1))]), err0 = ESUCCESS, n1 = 0

Heuristic symbolic execution applied rule assign right

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ buffered(m).leb = m; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ buffered(m).isbuf?; (s)% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)% ⊦ # avol[n, aleb] = # avol; (s)%⊦ awbuf-inv(avol, buffered(n)) → ( awbuf-inv(avol[n, mapped(buf)], buffered(n)) ↔ # avol[n].data ≤ LEB_SIZE → # buf ≤ LEB_SIZE); (ss)% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # subarray(buf, m, n) = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n → ¬ n < m; (s)