[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 9 from proof writepage-prepost (previous step)

asynced0 ↔ asynced, F0 = F, buf = mkbuf(VFS_PAGE_SIZE), dirs0 = dirs, files1 = files, inode0 = mkinode(m0, md0, boolvar, m2, m3, m4), m5 = m1, md1 = md, n4 = n2, n5 = n3, σ0 = σ, ((m0 =>mkfile(n2, md, m1, σ) * F))(files), ((mkinode(m0, md0, boolvar, m2, m3, m4).ino =>mkfile(n2, md, m1, σ) * F))(files), afs-cons(dirs, files), m0 ∈ files, n0 + n1 ≤ VFS_PAGE_SIZE, m + n1 ≤ # buf1 ⊦ [afs_readpage#(mkinode(m0, md0, boolvar, m2, m3, m4), n3, dirs, files, asynced; buf, err)] ( err = ESUCCESS ∧ ⌜buf⌝ = (σ0 from n5 * VFS_PAGE_SIZE) to VFS_PAGE_SIZE ∨ ⌊err⌋ → [if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); files0 := files; if err = ESUCCESS then {buf := copy(buf1, m, buf, n0, n1); afs_writepage#(mkinode(m0, md0, boolvar, m2, m3, m4), n3, buf, dirs; err, files; asynced)}] ( err = ESUCCESS ∧ ((m0 =>mkfile(n2, md, m1, (σ to n3 * VFS_PAGE_SIZE + n0) + ((⌜buf1⌝ from m) to n1) + (σ from n3 * VFS_PAGE_SIZE + n0 + n1)) * F) )(files) ∨ ⌊err⌋ ∧ files0 = files))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
buf = mkbuf(VFS_PAGE_SIZE), ((m0 =>mkfile(n2, md, m1, σ) * F))(files), afs-cons(dirs, files), m0 ∈ files, m + n1 ≤ # buf1, n0 + n1 ≤ VFS_PAGE_SIZE ⊦ [afs_readpage#(mkinode(m0, md0, boolvar, m2, m3, m4), n3, dirs, files, asynced; buf, err)] ( err = ESUCCESS ∧ ⌜buf⌝ = (σ from n3 * VFS_PAGE_SIZE) to VFS_PAGE_SIZE ∨ ⌊err⌋ → [if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); files0 := files; if err = ESUCCESS then {buf := copy(buf1, m, buf, n0, n1); afs_writepage#(mkinode(m0, md0, boolvar, m2, m3, m4), n3, buf, dirs; err, files; asynced)}] ( err = ESUCCESS ∧ ((m0 =>mkfile(n2, md, m1, (σ to n3 * VFS_PAGE_SIZE + n0) + ((⌜buf1⌝ from m) to n1) + (σ from n3 * VFS_PAGE_SIZE + n0 + n1)) * F) )(files) ∨ ⌊err⌋ ∧ files0 = files))

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)