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Proof step 20 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(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 ∧ write-inv(n, n + n0, buf, 0, files[ino].content, files[ino].content)) ∧ files1 -- ino = files -- ino ;⌊err0⌋ ) ∧ inode0 = mkinode(ino, md0, false, # links(ino, dirs), 0, m)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ write-inv(n0, n1, buf, n, content0, content1) ↔ content1.stream = (content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n)
Proof step 22:
⟨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)

Rule argument

spec: <toplevel> name: write-inv seq: ⊦ write-inv(n0, n1, buf, n, content0, content1) ↔ content1.stream = (content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n) subst: [content1, content0, n, buf, n1, n0] → [files[ino].content, files[ino].content, 0, buf, n + n0, n] flags: <all paths>

Additional information

Used terms: files[ino].content, files[ino].content, 0, buf, n + n0, n