[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 199 from proof eq-io-truncate (previous step)

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

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 200:
files1[m] = mkfile(m0, md0, m1, content0), m ∈ files1, buf-opt0.some? → # buf-opt0.buf = VFS_PAGE_SIZE ⊦ ⟨choose err0 with ⌊err0⌋ in err := err0; asynced := ?⟩ ( mkinode(m, md, false, m1, 0, m2) = (m ∈ dirs1 ⊃ mkinode(m, dirs1[m].meta, true, dirs1[m].nlink, dirs1[m].nsubdirs, dirs1[m].size);mkinode(m, md, false, m1, 0, n0)) ∧ ¬ boolvar ∧ err = ESUCCESS ∧ files1 = files1[m, mkfile(n0, md, m1, content0 upto min(n0, m2))]), ⟨let ino = m, content = content0, buf = ? in {pageno0 := m2 % VFS_PAGE_SIZE, pageno := min(n0, m2); boolvar := m2 ≤ n0 ∧ pageno0 ≠ 0 ∧ (m2 / VFS_PAGE_SIZE ∈ content ∨ buf-opt0.some?); buf-opt := buf-opt0; 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)}; files := files1[ino, 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, files)}; inode := (m ∈ dirs1 ⊃ mkinode(m, dirs1[m].meta, true, dirs1[m].nlink, dirs1[m].nsubdirs, dirs1[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[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, md, false, m1, 0, n0)) ∧ ¬ boolvar ∧ err = ESUCCESS ∧ dirs1 = dirs0 ∧ files = files1[m, mkfile(n0, md, m1, content0 upto min(n0, m2))]), m2 ≤ n0 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ (m2 / VFS_PAGE_SIZE ∈ content0 ∨ buf-opt0.some?)

Rule argument

pos: right 1

Additional information

Used simplifier rules: fail#(; ; ERR){choose ERR0 with ⌊ERR0⌋ in ERR := ERR0};