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Proof step 57 from proof read-inv-rec (previous step)

# buf1 = n4 + n + min(n3, n6, n1), # buf0 = # buf1, n0 + n = m0 * VFS_PAGE_SIZE + n5, VFS_PAGE_SIZE = n6 + n5, files[ino] = mkfile(n1 + n0 + n, md, # links(ino, dirs), content), n2 < # buf1, n2 < n + min(n3, n6, n1), ⌜n2⌝ < ⌜n⌝ + ⌜min(n3, n6, n1)⌝ + #(⌜buf0⌝ from n + min(n3, n6, n1)), n5 < VFS_PAGE_SIZE, afs-cons(dirs, files), ino ∈ files, min(n3, n6, n1) + n ≤ # buf1, n3 + n ≤ # buf1, n + min(n3, n6, n1) ≤ # buf1, n5 + min(n3, n6, n1) ≤ VFS_PAGE_SIZE, min(n3, n6, n1) ≤ n6 ⊦ (((content.stream from n0) to n) + ((content.stream from n0 + n) to min(n3, n6, n1)) + (⌜buf0⌝ from n + min(n3, n6, n1)))[n2] = getbyte(n0 + n2, content), n6 = 0, ⌜n2⌝ < #((content.stream from n0) to n)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 58:
# buf0 = # buf1, # buf1 = n4 + n + min(n3, n6, n1), n0 + n = m0 * VFS_PAGE_SIZE + n5, VFS_PAGE_SIZE = n6 + n5, files[ino] = mkfile(n1 + n0 + n, md, # links(ino, dirs), content), n5 < VFS_PAGE_SIZE, ⌜n2⌝ < ⌜n⌝ + ⌜min(n3, n6, n1)⌝ + #(⌜buf0⌝ from n + min(n3, n6, n1)), n2 < n + min(n3, n6, n1), n2 < # buf1, n < # buf1, afs-cons(dirs, files), ino ∈ files, min(n3, n6, n1) ≤ n6, n5 + min(n3, n6, n1) ≤ VFS_PAGE_SIZE, n + min(n3, n6, n1) ≤ # buf1, n3 + n ≤ # buf1, min(n3, n6, n1) + n ≤ # buf1, n ≤ n2 ⊦ n4 + min(n3, n6, n1) = 0, (((content.stream from n0 + n) to min(n3, n6, n1)) + (⌜buf0⌝ from n + min(n3, n6, n1)))[n2 - n] = getbyte(n0 + n2, content), n1 = 0, n3 = 0, n6 = 0

Rule argument

Additional information

Used simplifier rules: lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ min(n0, n1, n2) = 0 ↔ n0 = 0 ∨ n1 = 0 ∨ n2 = 0; (ws)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < m + n ↔ n ≠ 0; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s)%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]% ⊦ ⌜m⌝ .n = m; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ ¬ ∞ < n∞; (s)% ⊦ #(content.stream from n) = ∞; (s)% ⊦ ¬ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ2[m - (# σ0).n]; (s)