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Proof step 466 from proof refine-truncate (previous step)

boolvar4 ↔ boolvar, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, fs0[ri[inodekey(m)]] = inodenode(key, md0, false, m3, 0, m5), adr = adr3, adr0 = adr2, adr4 = adr1, adr6 = adr5, dirs = abs-dirs(fs0, ri), err = ESUCCESS, err0 = err, files = abs-files(fs0, ri), fs = fs0[adr4, nd1][adr0, nd0][adr, nd], log = ((log0 + adr4) + adr0) + adr, m1 = m, nd = nd2.data:= fill(nd2.data, zero, m2 % VFS_PAGE_SIZE, n0), nd0 = inodenode(inodekey(m), md, false, m3, 0, n), nd1 = truncnode(inodekey(m), m2), nd2 = fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]], ro = orphans(fs0, ri), ro0 = orphans(fs0, ri), fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data?, nd2.data?, orphans(fs0, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)), file-node-cons(fs0, ri), log-cons(log0, fs0), new(adr1 ' + (adr2 ' + adr3), fs0), node-cons(nd1.key, nd1), node-cons(nd0.key, nd0), node-cons(nd.key, nd), orphans-cons(fs0, ri, orphans(fs0, ri)), replay-cons-strong(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri-cons(ri, fs0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, orphans(fs0, ri), fi, fo, log0), inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs0, ri[datakey(m, m2 / VFS_PAGE_SIZE)] ∈ fs0, datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri, m2 ≤ n, m2 % VFS_PAGE_SIZE + n0 ≤ # nd2.data, asynced → boolvar0 ⊦ [aubifs_core_index_store#(datakey(m1, m2 / VFS_PAGE_SIZE), adr, fi, ro0, fo, fs, log, boolvar4; ri); buf-opt := buf-opt0; boolvar1 := boolvar2; nd2.data := fill(nd2.data, zero, m2 % VFS_PAGE_SIZE, n0); inode := mkinode(m1, md, false, m3, 0, m2); if err0 = ESUCCESS then {aubifs_core_index_store#(inodekey(m1), adr0, fi, ro0, fo, fs, log, boolvar4; ri); aubifs_core_index_truncate#(inodekey(m), min(n, m2), fi, ro0, fo, fs, log, boolvar4; ri); boolvar1 := true; inode := mkinode (inode.ino, inodenode(inodekey(m), md, false, m3, 0, n).meta, inodenode(inodekey(m), md, false, m3, 0, n).directory, inodenode(inodekey(m), md, false, m3, 0, n).nlink, inodenode(inodekey(m), md, false, m3, 0, n).nsubdirs, inodenode(inodekey(m), md, false, m3, 0, n).size); if boolvar1 then buf-opt := some(nd2.data)}] ( ubifs-cons(fs, ri, ro0, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro0, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro0) ∧ ri-inj(ri) ∧ log-cons(log, fs) → ⟨p_inode := mkinode(m, md, false, m3, 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, p_inode, boolvar2, err1, dirs, files, asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro0) ∧ (asynced → boolvar4) ∧ buf-opt = buf-opt0 ∧ inode = p_inode ∧ (boolvar1 ↔ boolvar2) ∧ err0 = err1)), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, buf-opt0.some?, dups(adr1 ' + adr2 ' + adr3 ')

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 467:
VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, fs0[ri[inodekey(m)]] = inodenode(key, md0, false, m3, 0, m5), dirs = abs-dirs(fs0, ri), files = abs-files(fs0, ri), fs = fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m3, 0, n)] [adr3, fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0) ], nd2 = fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]], ro = orphans(fs0, ri), m2 % VFS_PAGE_SIZE ≠ 0, adr1 ≠ adr2, adr1 ≠ adr3, adr2 ≠ adr3, m ≠ 0, fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data?, fo.inodes?, orphans(fs0, ri).inodes?, afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)), file-node-cons(fs0, ri), log-cons(log0, fs0), node-cons ((fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0)).key, fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0)), orphans-cons(fs0, ri, orphans(fs0, ri)), replay-cons-strong(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri-cons(ri, fs0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, orphans(fs0, ri), fi, fo, log0), datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri, ri[datakey(m, m2 / VFS_PAGE_SIZE)] ∈ fs0, ri[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri, m2 ≤ n, ¬ buf-opt0.some?, ¬ adr3 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr1 ∈ fs0, asynced → boolvar0 ⊦ [aubifs_core_index_store#(datakey(m, m2 / VFS_PAGE_SIZE), adr3, fi, orphans(fs0, ri), fo, fs, ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar4; ri); buf-opt := buf-opt0; boolvar1 := boolvar2; nd2.data := fill(nd2.data, zero, m2 % VFS_PAGE_SIZE, n0); inode := mkinode(m, md, false, m3, 0, m2); log := ((log0 + adr1 ') + adr2 ') + adr3 '; err := ESUCCESS; if err = ESUCCESS then {aubifs_core_index_store#(inodekey(m), adr2, fi, ro, fo, fs, log, boolvar4; ri); aubifs_core_index_truncate#(inodekey(m), min(n, m2), fi, ro, fo, fs, log, boolvar4; ri); boolvar1 := true; inode := mkinode (inode.ino, inodenode(inodekey(m), md, false, m3, 0, n).meta, inodenode(inodekey(m), md, false, m3, 0, n).directory, inodenode(inodekey(m), md, false, m3, 0, n).nlink, inodenode(inodekey(m), md, false, m3, 0, n).nsubdirs, inodenode(inodekey(m), md, false, m3, 0, n).size); if boolvar1 then buf-opt := some(nd2.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) ∧ ri-inj(ri) ∧ log-cons(log, fs) → ⟨p_inode := mkinode(m, md, false, m3, 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, p_inode, boolvar2, err1, dirs, files, asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro) ∧ (asynced → boolvar4) ∧ buf-opt = buf-opt0 ∧ inode = p_inode ∧ (boolvar1 ↔ boolvar2) ∧ err = err1))

Rule argument

Additional information

Used simplifier rules: ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)% ⊦ m ≤ m; (s)%ubifs-file-notdir: ⊦ datakey(ino, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → ¬ fs[ri[inodekey(ino)]].directory; (forward) from specification aubifs-inv%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ adr ∈ adr0 ' ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' + ax ↔ adr = adr0 ∨ adr ∈ ax; (s)% ⊦ dups(adr ' + adr0 ') ↔ adr = adr0; (s)% ⊦ dups(adr ' + ax) ↔ dups(ax) ∨ adr ∈ ax; (ws)% ⊦ new(adr ', fs) ↔ ¬ adr ∈ fs; (s)% ⊦ new(adr ' + log, fs) ↔ ¬ adr ∈ fs ∧ new(log, fs); (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ ax + adr = ax + adr '; (s)% ⊦ node-cons(key0, truncnode(key1, n)) ↔ key0.inode?; (s)% ⊦ truncnode(key, m).key = key; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)%⊦ node-cons(key0, inodenode(key1, md, boolvar, n, n0, m)) ↔ key0.inode? ∧ key0.ino ≠ 0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)%⊦ datakey(m, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → # fs[ri[datakey(m, n)]].data = VFS_PAGE_SIZE; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)