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Proof step 332 from proof refine-truncate (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, 0 = fs[ri[inodekey(m)]].nsubdirs, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri) [m, mkfile (fs[ri[inodekey(m)]].size, fs[ri[inodekey(m)]].meta, fs[ri[inodekey(m)]].nlink, abs-content(m, fs, ri)[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE)] upto m2) ], m2 % VFS_PAGE_SIZE ≠ 0, fs[ri[inodekey(m)]].inode?, fo.inodes?, orphans(fs, ri).inodes?, buf-opt0.some?, 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, ¬ fs[ri[inodekey(m)]].directory, asynced → boolvar0, ∀ adr1, adr2, adr3. adr1 ∈ fs ∨ adr2 ∈ fs ∨ adr3 ∈ fs ∨ adr1 = adr2 ∨ adr1 = adr3 ∨ adr2 = adr3 ⊦ ⟨afs_inode_sync#(mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, 0, n); dirs, files); inode := getinode(mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, 0, m2).ino, dirs, files); err := ESUCCESS; asynced := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar4) ∧ buf-opt0 = some(fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE)) ∧ mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, 0, m2) = inode ∧ boolvar2 ∧ ENOSPC = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced → boolvar4) ∧ ENOSPC = err)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 333:
# buf-opt0.buf = VFS_PAGE_SIZE, 0 = fs[ri[inodekey(m)]].nsubdirs, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri) [m, mkfile (fs[ri[inodekey(m)]].size, fs[ri[inodekey(m)]].meta, fs[ri[inodekey(m)]].nlink, abs-content(m, fs, ri)[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ], fs[ri[inodekey(m)]].inode?, orphans(fs, ri).inodes?, fo.inodes?, buf-opt0.some?, 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, m2 % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE, asynced → boolvar0, ∀ adr1, adr2, adr3. adr1 ∈ fs ∨ adr2 ∈ fs ∨ adr3 ∈ fs ∨ adr1 = adr2 ∨ adr1 = adr3 ∨ adr2 = adr3 ⊦ ⟨afs_inode_sync#(mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, 0, n); dirs, files); inode := getinode(mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, 0, m2).ino, dirs, files); err := ESUCCESS; asynced := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar4) ∧ buf-opt0 = some(fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)) ∧ mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, 0, m2) = inode ∧ boolvar2 ∧ ENOSPC = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced → boolvar4) ∧ ENOSPC = err), m2 % VFS_PAGE_SIZE = 0, fs[ri[inodekey(m)]].directory

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, n1]

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, n1