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Proof step 70 from proof refine-truncate (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, 0 = fs0[ri0[inodekey(m)]].nsubdirs, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, buf-opt = some(fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE)), buf-opt1 = buf-opt0, dirs = abs-dirs(fs0, ri0), files = abs-files(fs0, ri0), p_inode = mkinode(m, md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2), m2 % VFS_PAGE_SIZE ≠ 0, adr1 ≠ adr2, adr1 ≠ adr3, adr2 ≠ adr3, m ≠ 0, fs0[ri0[inodekey(m)]].inode?, orphans(fs0, ri0).inodes?, fo.inodes?, buf-opt0.some?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2])), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ]), log-cons(log0, fs0), orphans-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2]), orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-inj ( ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2])), ri-inj(ri0), ri-inj(fi), ubifs-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, m2 ≤ n1, ¬ fs0[ri0[inodekey(m)]].directory, ¬ adr3 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr1 ∈ fs0, asynced → boolvar0 ⊦ ⟨afs_truncate#(n1, m2 / VFS_PAGE_SIZE; buf-opt0, p_inode, boolvar2, err0, dirs, files, asynced)⟩ ( dirs = abs-dirs (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt1.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2]) ∧ files = abs-files (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt1.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2])) ∧ orphans (abs-dirs (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt1.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2]), abs-files (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt1.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2])) = abs-keys(orphans(fs0, ri0)) ∧ (asynced → boolvar4) ∧ buf-opt = buf-opt0 ∧ mkinode(m, md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1) = p_inode ∧ boolvar2 ∧ ESUCCESS = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 71:
# buf-opt0.buf = VFS_PAGE_SIZE, 0 = fs0[ri0[inodekey(m)]].nsubdirs, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE = n2 + m2 % VFS_PAGE_SIZE, buf-opt = some(fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n2)), buf-opt1 = buf-opt0, dirs = abs-dirs(fs0, ri0), files = abs-files(fs0, ri0), p_inode = mkinode(m, md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2), fs0[ri0[inodekey(m)]].inode?, fo.inodes?, orphans(fs0, ri0).inodes?, buf-opt0.some?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2])), log-cons(log0, fs0), log-cons (log0, fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2]), orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-inj(fi), ri-inj(ri0), ri-inj ( ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2])), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, m2 ≤ n1, m2 % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE, asynced → boolvar0 ⊦ ⟨afs_truncate#(n1, m2 / VFS_PAGE_SIZE; buf-opt0, p_inode, boolvar2, err0, dirs, files, asynced)⟩ ( dirs = abs-dirs (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt1.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2]) ∧ files = abs-files (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt1.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2])) ∧ orphans (abs-dirs (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt1.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2]), abs-files (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt1.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2])) = abs-keys(orphans(fs0, ri0)) ∧ (asynced → boolvar4) ∧ buf-opt = buf-opt0 ∧ mkinode(m, md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1) = p_inode ∧ boolvar2 ∧ ESUCCESS = err0), m2 % VFS_PAGE_SIZE = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m = 0, fs0[ri0[inodekey(m)]].directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE, n]

Additional information

Used simplifier rules: ⊦ VFS_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ m % n ≤ n; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE, n