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Proof step 53 from proof eq-io-truncate (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, boolvar ↔ m2 ≤ n0 ∧ pageno0 ≠ 0 ∧ (m2 / VFS_PAGE_SIZE ∈ content ∨ buf-opt.some?), VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, files1[m] = mkfile(m0, md0, m1, content0), content = content0, ino = m, pageno = min(n0, m2), pageno0 = m2 % VFS_PAGE_SIZE, buf-opt.some?, m ∈ files1, m2 ≤ n0, m2 ≤ n0 → pageno0 ≠ 0 → VFS_PAGE_SIZE ≠ 0 ⊦ ⟨buf-opt0 := some(fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n1)); files0 := files1[m, mkfile(n0, md, m1, content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2)]; if boolvar then {pageno1 := m2 / VFS_PAGE_SIZE; if buf-opt.some? then buf := buf-opt.buf else buf := files1[ino].content[pageno1]; buf := fill(buf, zero, pageno0, VFS_PAGE_SIZE - pageno0); content[pageno1] := buf; buf-opt := some(buf)}; files1[ino].content := content upto pageno; let new_inode = mkinode(m, md, false, m1, 0, m2) in {new_inode.size := n0; dirs0 := dirs1; afs_inode_sync#(new_inode; dirs1, files1)}; inode := (m ∈ dirs1 ⊃ mkinode(m, dirs1[m].meta, true, dirs1[m].nlink, dirs1[m].nsubdirs, dirs1[m].size) ;mkinode(m, files1[m].meta, false, files1[m].nlink, 0, files1[m].size) ); err := ESUCCESS; asynced := ?⟩ ( buf-opt = buf-opt0 ∧ inode = (m ∈ dirs0 ⊃ mkinode(m, dirs0[m].meta, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size) ;mkinode(m, files0[m].meta, false, files0[m].nlink, 0, files0[m].size) ) ∧ boolvar ∧ err = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files0), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 54:
# buf-opt.buf = VFS_PAGE_SIZE, boolvar ↔ m2 ≤ n0 ∧ pageno0 ≠ 0 ∧ (m2 / VFS_PAGE_SIZE ∈ content ∨ buf-opt.some?), VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, files1[m] = mkfile(m0, md0, m1, content0), buf-opt0 = some(fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n1)), content = content0, ino = m, pageno = min(n0, m2), pageno0 = m2 % VFS_PAGE_SIZE, buf-opt.some?, m ∈ files1, m2 ≤ n0, m2 % VFS_PAGE_SIZE + n1 ≤ # buf-opt.buf, m2 ≤ n0 → pageno0 ≠ 0 → VFS_PAGE_SIZE ≠ 0 ⊦ ⟨files0 := files1[m, mkfile(n0, md, m1, content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2)]; if boolvar then {pageno1 := m2 / VFS_PAGE_SIZE; if buf-opt.some? then buf := buf-opt.buf else buf := files1[ino].content[pageno1]; buf := fill(buf, zero, pageno0, VFS_PAGE_SIZE - pageno0); content[pageno1] := buf; buf-opt := some(buf)}; files1[ino].content := content upto pageno; let new_inode = mkinode(m, md, false, m1, 0, m2) in {new_inode.size := n0; dirs0 := dirs1; afs_inode_sync#(new_inode; dirs1, files1)}; inode := (m ∈ dirs1 ⊃ mkinode(m, dirs1[m].meta, true, dirs1[m].nlink, dirs1[m].nsubdirs, dirs1[m].size) ;mkinode(m, files1[m].meta, false, files1[m].nlink, 0, files1[m].size) ); err := ESUCCESS; asynced := ?⟩ ( buf-opt = buf-opt0 ∧ inode = (m ∈ dirs0 ⊃ mkinode(m, dirs0[m].meta, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size) ;mkinode(m, files0[m].meta, false, files0[m].nlink, 0, files0[m].size) ) ∧ boolvar ∧ err = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files0), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0

Rule argument

Additional information

Used simplifier rules: ⊦ VFS_PAGE_SIZE ≠ 0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → ¬ n < m; (s)