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Proof step 223 from proof write-prepost (previous step)

⟨afs_truncate#(n0 + m0, (n0 + m0) / VFS_PAGE_SIZE; buf-opt, inode, isdir, err2, dirs1, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (isdir ↔ isdir0) ∧ err2 = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), files0 -- m = files -- m, files1 -- m = files -- m, of1[fd] = mkfile(m, mode, m0), files1[m] = mkfile(n0 + m0, md, # links(m, dirs1), content0), files0[m] = mkfile(n0 + m0, md, # links(m, dirs1), content), files[m] = mkfile(n0 + m0, md, m3, content1), buf-opt = none, err2 = ESUCCESS, content.stream from n0 + m0 = σ⊥, inode = mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), inode0 = mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), content0.stream to n0 + m0 = content.stream to n0 + m0, n0 ≠ 0, n1 ≠ 0, (content.stream to m0) + (⌜buf⌝ to ino) + (content.stream from m0 + ino) to n0 + m0 ≠ ⌜copy(buf, 0, (content.stream to n0 + m0).buf, m0, n0)⌝ , n0 < ino, afs-cons(dirs1, files1), of-cons(of1, dirs1, files1), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), buf, 0, dirs0, files0, files0), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), buf, ino, dirs0, files0, files), files1 ~ files0, m ∈ files1, m ∈ files, fd ∈ of1, n1 ≤ # buf, ⌊err0⌋ , err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ mode ≠ MODE_W ∧ mode ≠ MODE_RW

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 224:
⊦ n0 + m ≤ # buf0 ∧ n1 + m ≤ # buf1 → ⌜copy(buf0, n0, buf1, n1, m)⌝ = (⌜buf1⌝ to n1) + ((⌜buf0⌝ from n0) to m) + ((⌜buf1⌝ from n1 + m) to (# buf1 - n1 + m))
Proof step 225:
⟨afs_truncate#(n0 + m0, (n0 + m0) / VFS_PAGE_SIZE; buf-opt, inode, isdir, err2, dirs1, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (isdir ↔ isdir0) ∧ err2 = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), files1 -- m = files -- m, files0 -- m = files -- m, files[m] = mkfile(n0 + m0, md, m3, content1), files0[m] = mkfile(n0 + m0, md, # links(m, dirs1), content), files1[m] = mkfile(n0 + m0, md, # links(m, dirs1), content0), of1[fd] = mkfile(m, mode, m0), buf-opt = none, err2 = ESUCCESS, content.stream from n0 + m0 = σ⊥, inode = mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), inode0 = mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), content0.stream to n0 + m0 = content.stream to n0 + m0, n0 < ino, afs-cons(dirs1, files1), of-cons(of1, dirs1, files1), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), buf, ino, dirs0, files0, files), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), buf, 0, dirs0, files0, files0), files1 ~ files0, fd ∈ of1, m ∈ files, m ∈ files1, n1 ≤ # buf, ⌊err0⌋ , err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ n0 = 0, n1 = 0, (content.stream to m0) + (⌜buf⌝ to ino) + (content.stream from m0 + ino) to n0 + m0 = ⌜copy(buf, 0, (content.stream to n0 + m0).buf, m0, n0)⌝ , mode ≠ MODE_W ∧ mode ≠ MODE_RW, 0 + n0 ≤ # buf ∧ m0 + n0 ≤ # (content.stream to n0 + m0).buf
Proof step 228:
⟨afs_truncate#(n0 + m0, (n0 + m0) / VFS_PAGE_SIZE; buf-opt, inode, isdir, err2, dirs1, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (isdir ↔ isdir0) ∧ err2 = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), files1 -- m = files -- m, files0 -- m = files -- m, files[m] = mkfile(n0 + m0, md, m3, content1), files0[m] = mkfile(n0 + m0, md, # links(m, dirs1), content), files1[m] = mkfile(n0 + m0, md, # links(m, dirs1), content0), of1[fd] = mkfile(m, mode, m0), buf-opt = none, err2 = ESUCCESS, content.stream from n0 + m0 = σ⊥, inode = mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), inode0 = mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), content0.stream to n0 + m0 = content.stream to n0 + m0, n0 < ino, afs-cons(dirs1, files1), of-cons(of1, dirs1, files1), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), buf, ino, dirs0, files0, files), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), buf, 0, dirs0, files0, files0), files1 ~ files0, fd ∈ of1, m ∈ files, m ∈ files1, n1 ≤ # buf, 0 + n0 ≤ # buf, m0 + n0 ≤ # (content.stream to n0 + m0).buf, ⌊err0⌋ , err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ n0 = 0, n1 = 0, (content.stream to m0) + (⌜buf⌝ to ino) + (content.stream from m0 + ino) to n0 + m0 = (⌜(content.stream to n0 + m0).buf⌝ to m0) + ((⌜buf⌝ from 0) to n0) + ((⌜(content.stream to n0 + m0).buf⌝ from m0 + n0) to (# (content.stream to n0 + m0).buf - m0 + n0)), mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

spec: afs-stream name: copy-stream-append seq: ⊦ n0 + m ≤ # buf0 ∧ n1 + m ≤ # buf1 → ⌜copy(buf0, n0, buf1, n1, m)⌝ = (⌜buf1⌝ to n1) + ((⌜buf0⌝ from n0) to m) + ((⌜buf1⌝ from n1 + m) to (# buf1 - n1 + m)) subst: [m, n1, buf1, n0, buf0] → [n0, m0, (content.stream to n0 + m0).buf, 0, buf] flags: <all paths>

Additional information

Used terms: n0, m0, (content.stream to n0 + m0).buf, 0, buf