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Proof step 854 from proof refine-truncate (previous step)

0 = fs[ri[inodekey(m)]].nsubdirs, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), m0 = fs[ri[inodekey(m)]].nlink, nd0 = inodenode(inodekey(m), md, false, fs[ri[inodekey(m)]].nlink, 0, n), ro = orphans(fs, ri), m2 % VFS_PAGE_SIZE ≠ 0, fs[ri[inodekey(m)]].inode?, orphans(fs, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs, m2 ≤ n, ¬ fs[ri[inodekey(m)]].directory, ¬ buf-opt0.some?, ¬ datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri, asynced → boolvar4 ⊦ [aubifs_core_journal_add2#(truncnode(inodekey(m), m2), nd0, ri, fi, orphans(fs, ri), fo; adr1, adr0, fs, log; boolvar4, err); buf-opt := buf-opt0; boolvar1 := boolvar2; inode := mkinode(m, md, false, m0, 0, m2); if err = ESUCCESS then {aubifs_core_index_store#(inodekey(m), adr0, fi, ro, fo, fs, log, boolvar4; ri); aubifs_core_index_truncate#(inodekey(m), min(n, m2), fi, ro, fo, fs, log, boolvar4; ri); boolvar1 := false; inode := mkinode(inode.ino, nd0.meta, nd0.directory, nd0.nlink, nd0.nsubdirs, nd0.size); if boolvar1 then buf-opt := some(nd.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, 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))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 855:
0 = m3, fs[ri[inodekey(m)]] = inodenode(key, md0, boolvar, m1, m3, m4), ¬ boolvar, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), m0 = m1, nd0 = inodenode(inodekey(m), md, false, m1, 0, n), ro = orphans(fs, ri), fs[ri[inodekey(m)]].inode?, fo.inodes?, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, m2 ≤ n, asynced → boolvar4 ⊦ [aubifs_core_journal_add2#(truncnode(inodekey(m), m2), nd0, ri, fi, orphans(fs, ri), fo; adr1, adr0, fs, log; boolvar4, err); buf-opt := buf-opt0; boolvar1 := boolvar2; inode := mkinode(m, md, false, m0, 0, m2); if err = ESUCCESS then {aubifs_core_index_store#(inodekey(m), adr0, fi, ro, fo, fs, log, boolvar4; ri); aubifs_core_index_truncate#(inodekey(m), min(n, m2), fi, ro, fo, fs, log, boolvar4; ri); boolvar1 := false; inode := mkinode(inode.ino, nd0.meta, nd0.directory, nd0.nlink, nd0.nsubdirs, nd0.size); if boolvar1 then buf-opt := some(nd.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, 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)), m2 % VFS_PAGE_SIZE = 0, buf-opt0.some?, datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri

Rule argument

spec: node name: elim-03 seq: ⊦ nd.inode? → ( ( ( ( (key = nd.key ∧ md = nd.meta) ∧ (boolvar ↔ nd.directory)) ∧ m = nd.nlink) ∧ m0 = nd.nsubdirs) ∧ m1 = nd.size ↔ nd = inodenode(key, md, boolvar, m, m0, m1)) subst: [nd, key, md, boolvar, m, m0, m1] → [fs[ri[inodekey(m)]], key, md0, boolvar, m1, m3, m4]

Additional information

Used simplifier rules: ⊦ nd.inode? → ( ( ( ( (key = nd.key ∧ md = nd.meta) ∧ (boolvar ↔ nd.directory)) ∧ m = nd.nlink) ∧ m0 = nd.nsubdirs) ∧ m1 = nd.size ↔ nd = inodenode(key, md, boolvar, m, m0, m1)); (elim) Used terms: fs[ri[inodekey(m)]], key, md0, boolvar, m1, m3, m4