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Proof step 31 from proof write-inode-inv (previous step)

files1 -- ino = files0 -- ino, files1[ino] = mkfile(m, md, # links(ino, dirs), content), files0[ino] = mkfile(m, md, m0, content0), afs-cons(dirs, files1), write-inv(0, n1, buf, n, content0, content), ROOT_INO ∈ dirs, ino ∈ files1, ino ∈ files0, n ≤ n1, n1 ≤ # buf, n ≤ # buf, ino0 ∈ files1 → ¬ ino0 ∈ dirs ∧ files1[ino0].nlink = # links(ino0, dirs), ino0 ∈ dirs ∧ ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → dirs[ino0].entries = ∅, ino0 ∈ dirs → dirs[ino0].nlink = # links(ino0, dirs) ∧ dirs[ino0].nlink ≤ 1 ∧ dirs[ino0].size = # dirs[ino0].entries ∧ dirs[ino0].nsubdirs = # subdirs(ino0, dirs), ino0 ∈ dirs ∧ name ∈ dirs[ino0].entries → dirs[ino0].entries[name] ∈ dirs ∨ dirs[ino0].entries[name] ∈ files1, ino0 ∈ files1 ∧ n0 ∈ files1[ino0].content → # files1[ino0].content[n0] = VFS_PAGE_SIZE ⊦ (ino0 ∈ files1 → ¬ ino0 ∈ dirs ∧ (ino0 = ino ⊃ mkfile(m + n, md, # links(ino, dirs), content);files1[ino0]).nlink = # links(ino0, dirs)) ∧ ( ino0 ∈ files1 ∧ n0 ∈ (ino0 = ino ⊃ mkfile(m + n, md, # links(ino, dirs), content);files1[ino0]).content → # (ino0 = ino ⊃ mkfile(m + n, md, # links(ino, dirs), content);files1[ino0]).content[n0] = VFS_PAGE_SIZE)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 32:
files1 -- ino = files0 -- ino, files0[ino] = mkfile(m, md, m0, content0), files1[ino] = mkfile(m, md, # links(ino, dirs), content), files1[ino0] = mkfile(m1, md0, m2, content1), afs-cons(dirs, files1), write-inv(0, n1, buf, n, content0, content), ino ∈ files0, ino ∈ files1, ROOT_INO ∈ dirs, n ≤ # buf, n1 ≤ # buf, n ≤ n1, ino0 ∈ files1 ∧ n0 ∈ content1 → # content1[n0] = VFS_PAGE_SIZE, ino0 ∈ dirs ∧ name ∈ dirs[ino0].entries → dirs[ino0].entries[name] ∈ dirs ∨ dirs[ino0].entries[name] ∈ files1, ino0 ∈ dirs → dirs[ino0].nlink = # links(ino0, dirs) ∧ dirs[ino0].nlink ≤ 1 ∧ dirs[ino0].size = # dirs[ino0].entries ∧ dirs[ino0].nsubdirs = # subdirs(ino0, dirs), ino0 ∈ dirs ∧ ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → dirs[ino0].entries = ∅, ino0 ∈ files1 → ¬ ino0 ∈ dirs ∧ m2 = # links(ino0, dirs) ⊦ (ino0 ∈ files1 → ¬ ino0 ∈ dirs ∧ (ino0 = ino ⊃ mkfile(m + n, md, # links(ino, dirs), content);files1[ino0]).nlink = # links(ino0, dirs)) ∧ ( ino0 ∈ files1 ∧ n0 ∈ (ino0 = ino ⊃ mkfile(m + n, md, # links(ino, dirs), content);files1[ino0]).content → # (ino0 = ino ⊃ mkfile(m + n, md, # links(ino, dirs), content);files1[ino0]).content[n0] = VFS_PAGE_SIZE)

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[ino0], m1, md0, m2, content1]

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[ino0], m1, md0, m2, content1