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Proof step 223 from proof inv-truncate (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, fs0[ri0[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, fs0[ri0[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro, VFS_PAGE_SIZE = n0 + m3 % VFS_PAGE_SIZE, fs0[ri0[inodekey(m)]].inode?, ro.inodes?, fo.inodes?, buf-opt.some?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, inodekey(ino) ∈ ri0, m3 ≤ n1 ⊦ m3 % VFS_PAGE_SIZE = 0, (adr3 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ;(adr2 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n1) ;(adr1 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ truncnode(inodekey(m), m3);fs0[(m = ino ⊃ adr2;ri0[inodekey(ino)])]) ) ) .nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro, adr1 = adr3, adr1 = adr2, adr2 = adr3, fs0[ri0[inodekey(m)]].directory, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 224:
# buf-opt.buf = VFS_PAGE_SIZE, fs0[ri0[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro, m0 = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, VFS_PAGE_SIZE = n0 + m3 % VFS_PAGE_SIZE, fs0[ri0[inodekey(m)]] = inodenode(key, md, boolvar, m0, m1, m2), ¬ boolvar, fs0[ri0[inodekey(m)]].inode?, fo.inodes?, ro.inodes?, buf-opt.some?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), inodekey(ino) ∈ ri0, inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, m3 ≤ n1 ⊦ m3 % VFS_PAGE_SIZE = 0, (adr3 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ;(adr2 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m), md0, false, m0, m1, n1) ;(adr1 = (m = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ truncnode(inodekey(m), m3);fs0[(m = ino ⊃ adr2;ri0[inodekey(ino)])]) ) ) .nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro, adr1 = adr2, adr1 = adr3, adr2 = adr3, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0

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] → [fs0[ri0[inodekey(m)]], key, md, boolvar, m0, m1, m2]

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: fs0[ri0[inodekey(m)]], key, md, boolvar, m0, m1, m2