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Proof step 22 from proof truncate-inv (previous step)

⟨afs_truncate#(m, m / VFS_PAGE_SIZE; buf-opt, inode, bv, err, dirs, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (bv ↔ bv0) ∧ err = err0 ∧ dirs = dirs0 ∧ files1 = files ∧ (asynced ↔ asynced0)), files1[ino] = mkfile(m, md0, # links(ino, dirs), content), buf-opt = none, inode = mkinode(ino, md0, false, # links(ino, dirs), 0, m), afs-cons(dirs0, files), afs-cons(dirs, files1), files1 ~ files, ino ∈ files1, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ (err0 = ESUCCESS ⊃ files[ino].content.stream from m = σ⊥ ∧ ( n0 ≤ # buf → ino ∈ files ∧ files[ino].size = m ∧ files[ino].content.stream = (files[ino].content.stream to n) + (⌜buf⌝ to 0) + (files[ino].content.stream from n + 0)) ∧ files1 -- ino = files -- ino ;⌊err0⌋ ) ∧ inode0 = mkinode(ino, md0, false, # links(ino, dirs), 0, m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
⟨afs_truncate#(m, m / VFS_PAGE_SIZE; buf-opt, inode, bv, err, dirs, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (bv ↔ bv0) ∧ err = err0 ∧ dirs = dirs0 ∧ files1 = files ∧ (asynced ↔ asynced0)), files1[ino] = mkfile(m, md0, # links(ino, dirs), content), buf-opt = none, inode = mkinode(ino, md0, false, # links(ino, dirs), 0, m), afs-cons(dirs, files1), afs-cons(dirs0, files), files1 ~ files, ino ∈ files1, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ (err0 = ESUCCESS ⊃ files[ino].content.stream from m = σ⊥ ∧ (n0 ≤ # buf → ino ∈ files ∧ files[ino].size = m) ∧ files1 -- ino = files -- ino ;⌊err0⌋ ) ∧ inode0 = mkinode(ino, md0, false, # links(ino, dirs), 0, m)

Rule argument

Additional information

Used simplifier rules: ¬ # σ0 < ⌜n⌝ ⊦ (σ0 to n) + (σ0 from n) = σ0 ↔ true; (ss)% ⊦ ¬ ∞ < n∞; (s)% ⊦ # content.stream = ∞; (s)%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]% ⊦ [] + σ0 = σ0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ σ0 to 0 = []; (s)