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Proof step 100 from proof inv-truncate (previous step)

files0[ino] = mkfile(m0, md, m3, content), files0[m] = mkfile(m1, md1, # links(m, dirs), content0), afs-cons(dirs, files0), m ∈ files0, ROOT_INO ∈ dirs, buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE, ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅, ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs), ino ∈ files0 → ¬ ino ∈ dirs ∧ m3 = # links(ino, dirs), ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files0 ⊦ m2 ≤ n ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ (m2 / VFS_PAGE_SIZE ∈ content0 ∨ buf-opt.some?), ( ino ∈ files0 → ¬ ino ∈ dirs ∧ (ino = m ⊃ mkfile(m1, md1, # links(m, dirs), content0 upto min(n, m2));mkfile(m0, md, m3, content)).nlink = # links(ino, dirs)) ∧ ( ino ∈ files0 ∧ n0 ∈ (ino = m ⊃ mkfile(m1, md1, # links(m, dirs), content0 upto min(n, m2));mkfile(m0, md, m3, content)).content → # (ino = m ⊃ mkfile(m1, md1, # links(m, dirs), content0 upto min(n, m2));mkfile(m0, md, m3, content)).content[n0] = VFS_PAGE_SIZE)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 101:
(ino = m ⊃ mkfile(m1, md1, # links(m, dirs), content0 upto min(n, m2));mkfile(m0, md, m3, content)) = mkfile(m4, md0, m5, content1), files0[m] = mkfile(m1, md1, # links(m, dirs), content0), files0[ino] = mkfile(m0, md, m3, content), afs-cons(dirs, files0), ROOT_INO ∈ dirs, m ∈ files0, ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files0, ino ∈ files0 → ¬ ino ∈ dirs ∧ m3 = # links(ino, dirs), ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅, buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE ⊦ (ino ∈ files0 → ¬ ino ∈ dirs ∧ m5 = # links(ino, dirs)) ∧ (ino ∈ files0 ∧ n0 ∈ content1 → # content1[n0] = VFS_PAGE_SIZE), m2 ≤ n ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ (m2 / VFS_PAGE_SIZE ∈ content0 ∨ buf-opt.some?)

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] → [(ino = m ⊃ mkfile (m1, md1, # links(m, dirs), content0 upto min(n, m2)) ;mkfile(m0, md, m3, content) ), m4, md0, m5, 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: (ino = m ⊃ mkfile(m1, md1, # links(m, dirs), content0 upto min(n, m2)) ;mkfile(m0, md, m3, content) ), m4, md0, m5, content1