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Proof step 17 from proof inv-write-buf (previous step)

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

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 18:
# 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

Rule argument

Additional information

Used simplifier rules: ⊦ buffered(m).leb = m; (s)% ⊦ buffered(m).isbuf?; (s)% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf).mapped?; (s)% ⊦ m < n → m ≤ n; (s)