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Proof step 39 from proof refine-truncate (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, boolvar4 ↔ boolvar, 0 = fs0[ri[inodekey(m)]].nsubdirs, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, adr = adr3, adr0 = adr2, adr4 = adr1, adr6 = adr5, dirs = abs-dirs(fs0, ri), err = ESUCCESS, files = abs-files(fs0, ri), fs = fs0[adr4, nd1][adr0, nd0][adr, nd], key = datakey(m, m2 / VFS_PAGE_SIZE), log = ((log0 + adr4) + adr0) + adr, m0 = fs0[ri[inodekey(m)]].nlink, nd = datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(datanode(datakey(m, m2 / VFS_PAGE_SIZE), buf-opt0.buf).data, zero, m2 % VFS_PAGE_SIZE, n0)), nd0 = inodenode(inodekey(m), md, false, m0, 0, n), nd1 = truncnode(inodekey(m), m2), ro = orphans(fs0, ri), ro0 = orphans(fs0, ri), datanode(datakey(m, m2 / VFS_PAGE_SIZE), buf-opt0.buf).data?, orphans(fs0, ri).inodes?, fo.inodes?, buf-opt0.some?, afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)), file-node-cons(fs0, ri), log-cons(log0, fs0), new(adr1 ' + (adr2 ' + adr3), fs0), orphans-cons(fs0, ri, orphans(fs0, ri)), replay-cons-strong(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, orphans(fs0, ri), fi, fo, log0), inodekey(m) ∈ ri, m2 ≤ n, m2 % VFS_PAGE_SIZE + n0 ≤ # datanode(datakey(m, m2 / VFS_PAGE_SIZE), buf-opt0.buf).data, asynced → boolvar0 ⊦ [aubifs_core_index_store#(key, adr, fi, ro0, fo, fs, log, boolvar4; ri); pageno0 := m2 % VFS_PAGE_SIZE; nd0 := inodenode(inodekey(m), md, false, m0, 0, n); buf-opt := buf-opt0; boolvar3 := boolvar2; inode := mkinode(m, md, false, m0, 0, m2); if err = ESUCCESS then {aubifs_core_index_store#(inodekey(m), adr0, fi, ro0, fo, fs, log, boolvar4; ri); aubifs_core_index_truncate#(inodekey(m), min(n, m2), fi, ro0, fo, fs, log, boolvar4; ri); boolvar3 := true; inode := mkinode(inode.ino, nd0.meta, nd0.directory, nd0.nlink, nd0.nsubdirs, nd0.size); nd := datanode(key, buf-opt.buf); if boolvar3 then buf-opt := some((nd.data:= fill(nd.data, zero, pageno0, VFS_PAGE_SIZE - pageno0)).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, m0, 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, p_inode, boolvar2, err0, 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 ∧ (boolvar3 ↔ boolvar2) ∧ err = err0)), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, fs0[ri[inodekey(m)]].directory, dups(adr1 ' + adr2 ' + adr3 ')

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
# buf-opt0.buf = VFS_PAGE_SIZE, 0 = fs0[ri[inodekey(m)]].nsubdirs, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, dirs = abs-dirs(fs0, ri), files = abs-files(fs0, ri), fs = fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri[inodekey(m)]].nlink, 0, n)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], m0 = fs0[ri[inodekey(m)]].nlink, ro = orphans(fs0, ri), m2 % VFS_PAGE_SIZE ≠ 0, adr1 ≠ adr3, adr1 ≠ adr2, adr2 ≠ adr3, orphans(fs0, ri).inodes?, fo.inodes?, buf-opt0.some?, afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)), file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, orphans(fs0, ri)), replay-cons-strong(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, orphans(fs0, ri), fi, fo, log0), inodekey(m) ∈ ri, m2 ≤ n, ¬ fs0[ri[inodekey(m)]].directory, ¬ adr1 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr3 ∈ 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); pageno0 := m2 % VFS_PAGE_SIZE; nd0 := inodenode(inodekey(m), md, false, m0, 0, n); buf-opt := buf-opt0; boolvar3 := boolvar2; inode := mkinode(m, md, false, m0, 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); boolvar3 := true; inode := mkinode(inode.ino, nd0.meta, nd0.directory, nd0.nlink, nd0.nsubdirs, nd0.size); nd := datanode(datakey(m, m2 / VFS_PAGE_SIZE), buf-opt.buf); if boolvar3 then buf-opt := some((nd.data:= fill(nd.data, zero, pageno0, VFS_PAGE_SIZE - pageno0)).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, m0, 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, p_inode, boolvar2, err0, 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 ∧ (boolvar3 ↔ boolvar2) ∧ err = err0))

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)%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)% ⊦ datanode(key, buf).data?; (s)% ⊦ 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)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)% ⊦ datanode(key, buf).data = buf; (s)