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Proof step 335 from proof inv-truncate (previous step)

m = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, VFS_PAGE_SIZE = n0 + m4 % VFS_PAGE_SIZE, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]] = datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf0), fs0[ri0[inodekey(m0)]] = inodenode(key1, md, false, m, m1, m2), fs0[ri0[dentrykey(ino, str)]].dentry?, fs0[ri0[inodekey(ino)]].directory, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), inodekey(m0) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, datakey(m0, m4 / VFS_PAGE_SIZE) ∈ ri0, ri0[datakey(m0, m4 / VFS_PAGE_SIZE)] ∈ fs0, ri0[dentrykey(ino, str)] ∈ fs0, dentrykey(ino, str) ∈ ri0, inodekey(fs0[ri0[dentrykey(ino, str)]].ino) ∈ ri0, inodekey(ino) ∈ ri0, m4 ≤ n1, ro ⊆ dom ri0 ⊦ m4 % VFS_PAGE_SIZE = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m0 = 0, (adr3 = (m0 = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(adr2 = (m0 = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m0), md0, false, m, m1, n1) ;(adr1 = (m0 = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ truncnode(inodekey(m0), m4);fs0[(m0 = ino ⊃ adr2;ri0[inodekey(ino)])]) ) ) .directory, buf-opt.some?, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr3 ∈ ri0, inodekey(fs0[ri0[dentrykey(ino, str)]].ino) ∈ ro, inodekey(ino) ∈ ro

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 336:
m = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, VFS_PAGE_SIZE = n0 + m4 % VFS_PAGE_SIZE, fs0[ri0[inodekey(m0)]] = inodenode(key1, md, false, m, m1, m2), fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]] = datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf0), fs0[ri0[dentrykey(ino, str)]] = dentrynode(key, m3), fs0[ri0[dentrykey(ino, str)]].dentry?, fs0[ri0[inodekey(ino)]].directory, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), inodekey(ino) ∈ ri0, inodekey(m3) ∈ ri0, dentrykey(ino, str) ∈ ri0, ri0[dentrykey(ino, str)] ∈ fs0, ri0[datakey(m0, m4 / VFS_PAGE_SIZE)] ∈ fs0, datakey(m0, m4 / VFS_PAGE_SIZE) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, inodekey(m0) ∈ ri0, m4 ≤ n1, ro ⊆ dom ri0 ⊦ m4 % VFS_PAGE_SIZE = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m0 = 0, (adr3 = (m0 = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ;(adr2 = (m0 = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m0), md0, false, m, m1, n1) ;(adr1 = (m0 = ino ⊃ adr2;ri0[inodekey(ino)]) ⊃ truncnode(inodekey(m0), m4);fs0[(m0 = ino ⊃ adr2;ri0[inodekey(ino)])]) ) ) .directory, buf-opt.some?, inodekey(ino) ∈ ro, inodekey(m3) ∈ ro, adr3 ∈ ri0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0

Rule argument

spec: node name: elim-02 seq: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)) subst: [nd, key, m] → [fs0[ri0[dentrykey(ino, str)]], key, m3]

Additional information

Used simplifier rules: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)); (elim) Used terms: fs0[ri0[dentrykey(ino, str)]], key, m3