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Proof step 31 from proof inv-truncate (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, fs[ri[inodekey(m0)]].nlink = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, VFS_PAGE_SIZE = n0 + m4 % VFS_PAGE_SIZE, inode = mkinode(m0, md, false, fs[ri[inodekey(m0)]].nlink, fs[ri[inodekey(m0)]].nsubdirs, m4), nd0 = inodenode(inodekey(m0), md, false, fs[ri[inodekey(m0)]].nlink, fs[ri[inodekey(m0)]].nsubdirs, n), m4 % VFS_PAGE_SIZE ≠ 0, fs[ri[inodekey(m0)]].inode?, fo.inodes?, ro.inodes?, buf-opt.some?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, ro, fi, fo, log), inodekey(m0) ∈ ri, ri[inodekey(m0)] ∈ fs, m4 ≤ n, ¬ fs[ri[inodekey(m0)]].directory ⊦ ⟪aubifs_core_journal_add3# (truncnode(inodekey(m0), m4), nd0, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf-opt.buf).data, zero, m4 % VFS_PAGE_SIZE, n0)), ri, fi, ro, fo ; adr1, adr0, adr, fs, log ; boolvar0, err); if err = ESUCCESS then aubifs_core_index_store#(datakey(m0, m4 / VFS_PAGE_SIZE), adr, fi, ro, fo, fs, log, boolvar0; ri); if err = ESUCCESS then {aubifs_core_index_store#(inodekey(m0), adr0, fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_truncate#(inodekey(m0), m4, fi, ro, fo, fs, log, boolvar0; ri); boolvar1 := true; inode := mkinode(inode.ino, nd0.meta, nd0.directory, nd0.nlink, nd0.nsubdirs, nd0.size); if boolvar1 then buf-opt0 := some (datanode (datakey(m0, m4 / VFS_PAGE_SIZE), fill(datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf-opt.buf).data, zero, m4 % VFS_PAGE_SIZE, n0)) .data)}⟫ (ubifs-cons(fs, ri, ro, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 32:
# buf-opt.buf = VFS_PAGE_SIZE, fs[ri[inodekey(m0)]].nlink = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, VFS_PAGE_SIZE = n0 + m4 % VFS_PAGE_SIZE, adr4 = adr1, inode = mkinode(m0, md, false, fs[ri[inodekey(m0)]].nlink, fs[ri[inodekey(m0)]].nsubdirs, m4), nd = datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf-opt.buf).data, zero, m4 % VFS_PAGE_SIZE, n0)), nd0 = inodenode(inodekey(m0), md, false, fs[ri[inodekey(m0)]].nlink, fs[ri[inodekey(m0)]].nsubdirs, n), nd1 = truncnode(inodekey(m0), m4), datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf-opt.buf).data?, fs[ri[inodekey(m0)]].inode?, ro.inodes?, fo.inodes?, buf-opt.some?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, ro, fi, fo, log), ri[inodekey(m0)] ∈ fs, inodekey(m0) ∈ ri, m4 % VFS_PAGE_SIZE + n0 ≤ # datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf-opt.buf).data, m4 ≤ n ⊦ ⟪if ri-cons(ri, fs) ∧ node-cons(nd1.key, nd1) ∧ node-cons(nd0.key, nd0) ∧ node-cons(nd.key, nd) then { choose adr1, adr2, adr3 with new(adr1 ' + (adr2 ' + adr3), fs) ∧ ¬ dups(adr1 ' + adr2 ' + adr3 ') in {adr4 := adr1, adr0 := adr2, adr := adr3; fs := fs[adr4, nd1][adr0, nd0][adr, nd], log := ((log + adr4) + adr0) + adr, err := ESUCCESS} ifnone err := ENOSPC or {fail#(; ; err); adr4 := ?, adr0 := ?, adr := ?}; boolvar := ?} else abort; boolvar0 := boolvar; if err = ESUCCESS then aubifs_core_index_store#(datakey(m0, m4 / VFS_PAGE_SIZE), adr, fi, ro, fo, fs, log, boolvar0; ri); if err = ESUCCESS then {aubifs_core_index_store#(inodekey(m0), adr0, fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_truncate#(inodekey(m0), m4, fi, ro, fo, fs, log, boolvar0; ri); boolvar1 := true; inode := mkinode(inode.ino, nd0.meta, nd0.directory, nd0.nlink, nd0.nsubdirs, nd0.size); if boolvar1 then buf-opt0 := some (datanode (datakey(m0, m4 / VFS_PAGE_SIZE), fill(datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf-opt.buf).data, zero, m4 % VFS_PAGE_SIZE, n0)) .data)}⟫ (ubifs-cons(fs, ri, ro, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro)), m4 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, fs[ri[inodekey(m0)]].directory

Rule argument

pos: right 1

Additional information

Used simplifier rules: aubifs_core_journal_add3# (ND1, ND2, ND3, RI, FI, RO, FO ; ADR1, ADR2, ADR3, FS, LOG ; CSYNCED, ERR ) {if ri-cons(RI, FS) ∧ node-cons(ND1.key, ND1) ∧ node-cons(ND2.key, ND2) ∧ node-cons(ND3.key, ND3) then { choose adr1, adr2, adr3 with new(adr1 ' + (adr2 ' + adr3), FS) ∧ ¬ dups(adr1 ' + adr2 ' + adr3 ') in {ADR1 := adr1, ADR2 := adr2, ADR3 := adr3; FS := FS[ADR1, ND1][ADR2, ND2][ADR3, ND3], LOG := ((LOG + ADR1) + ADR2) + ADR3, ERR := ESUCCESS} ifnone ERR := ENOSPC or {fail#(; ; ERR); ADR1 := ?, ADR2 := ?, ADR3 := ?}; CSYNCED := ?} else abort };% ⊦ datanode(key, buf).data = buf; (s)% ⊦ datanode(key, buf).data?; (s)% ⊦ 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)