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Proof step 28 from proof truncate-inv (previous step)

⟨afs_truncate_internal#(m, m / VFS_PAGE_SIZE; inode, buf-opt, ino0, ino, isdir, err, dirs, files1; asynced)⟩ ( inode = inode0 ∧ buf-opt = buf-opt1 ∧ ino0 = ino2 ∧ ino = ino3 ∧ (isdir ↔ isdir0) ∧ err = err0 ∧ dirs = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced1)), # links(ino1, dirs) = files1[ino1].nlink, files1[ino1] = mkfile(m, md0, files1[ino1].nlink, content), buf-opt = none, ino = 0, ino0 = 0, inode = mkinode(ino1, md0, false, files1[ino1].nlink, 0, m), afs-cons(dirs0, files0), afs-cons(dirs, files1), files1 ~ files0, ino1 ∈ files1, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ (err0 = ESUCCESS ⊃ files0[ino1].content.stream from m = σ⊥ ∧ (n0 ≤ # buf → ino1 ∈ files0 ∧ files0[ino1].size = m) ∧ files1 -- ino1 = files0 -- ino1 ;⌊err0⌋ ) ∧ inode0 = mkinode(ino1, md0, false, files1[ino1].nlink, 0, m)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 29:
⟨afs_truncate_internal#(m, m / VFS_PAGE_SIZE; inode, buf-opt, ino0, ino, isdir, err, dirs, files1; asynced)⟩ ( inode = inode0 ∧ buf-opt = buf-opt1 ∧ ino0 = ino2 ∧ ino = ino3 ∧ (isdir ↔ isdir0) ∧ err = err0 ∧ dirs = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced1)), # links(ino1, dirs) = m1, files1[ino1] = mkfile(m, md0, m1, content), files1[ino1] = mkfile(m0, md, m1, content0), buf-opt = none, ino = 0, ino0 = 0, inode = mkinode(ino1, md0, false, m1, 0, m), afs-cons(dirs, files1), afs-cons(dirs0, files0), files1 ~ files0, ino1 ∈ files1, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ (err0 = ESUCCESS ⊃ files0[ino1].content.stream from m = σ⊥ ∧ (n0 ≤ # buf → ino1 ∈ files0 ∧ files0[ino1].size = m) ∧ files1 -- ino1 = files0 -- ino1 ;⌊err0⌋ ) ∧ inode0 = mkinode(ino1, md0, false, m1, 0, m)

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files1[ino1], m0, md1, m1, content0]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files1[ino1], m0, md1, m1, content0