[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 170 from proof eq-io-truncate (previous step)

boolvar ↔ m2 ≤ n0 ∧ pageno0 ≠ 0 ∧ (m2 / VFS_PAGE_SIZE ∈ content0 ∨ buf-opt.some?), VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, files2[m] = mkfile(m3, md1, m4, content), ¬ boolvar, content0 = content, dirs0 = dirs1, files = files2[ino, files2[ino].content:= (content0 upto pageno)], ino = m, new_inode = mkinode(m, md, false, m4, 0, m2), pageno = min(n0, m2), pageno0 = m2 % VFS_PAGE_SIZE, m ∈ files2, m2 / VFS_PAGE_SIZE ∈ content, VFS_PAGE_SIZE ≤ # content[m2 / VFS_PAGE_SIZE], m2 ≤ n0, m2 ≤ n0 → pageno0 ≠ 0 → VFS_PAGE_SIZE ≠ 0 ⊦ ⟨afs_inode_sync#(new_inode.size:= n0; 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 = some(fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)) ∧ inode = (m ∈ dirs0 ⊃ mkinode(m, dirs0[m].meta, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size);mkinode(m, md, false, m4, 0, n0)) ∧ boolvar ∧ err = ESUCCESS ∧ dirs1 = dirs0 ∧ files = files2[m, mkfile(n0, md, m4, content[m2 / VFS_PAGE_SIZE, fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2)]), ⟨fail#(; ; err); asynced := ?⟩ ( buf-opt = some(fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)) ∧ mkinode(m, md, false, m4, 0, m2) = mkinode(m, dirs1[m].meta, true, dirs1[m].nlink, dirs1[m].nsubdirs, dirs1[m].size) ∧ boolvar0 ∧ err = ESUCCESS ∧ files2 = files2[m, mkfile(n0, md, m4, content[m2 / VFS_PAGE_SIZE, fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2)]), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, buf-opt.some?

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: min-comm: ⊦ min(n0, n1) = min(n1, n0); from specification min-max% ⊦ n0 ≤ n1 → min(n0, n1) = n0; (s)