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Proof step 27 from proof write-inode-inv (previous step)

files1 -- ino = files0 -- ino, files0[ino] = mkfile(m, md, m0, content0), files1[ino] = mkfile(m, md, # links(ino, dirs), content), afs-cons(dirs, files1), write-inv(0, n1, buf, n, content0, content), ino ∈ files0, ino ∈ files1, n ≤ # buf, n1 ≤ # buf, n ≤ n1 ⊦ afs-cons(dirs, files1[ino, mkfile(m + n, md, # links(ino, dirs), content)]) ∧ mkinode(ino, md, false, # links(ino, dirs), 0, m + n).ino ∈ files0[ino, mkfile(m + n, md, m0, content0)] ∧ mkinode(ino, md, false, # links(ino, dirs), 0, m + n).ino ∈ files1[ino, mkfile(m + n, md, # links(ino, dirs), content)] ∧ files0[ino, mkfile(m + n, md, m0, content0)][mkinode(ino, md, false, # links(ino, dirs), 0, m + n).ino].size = mkinode(ino, md, false, # links(ino, dirs), 0, m + n).size ∧ files1[ino, mkfile(m + n, md, # links(ino, dirs), content)][mkinode(ino, md, false, # links(ino, dirs), 0, m + n).ino].size = files0[ino, mkfile(m + n, md, m0, content0)][mkinode(ino, md, false, # links(ino, dirs), 0, m + n).ino].size ∧ files1[ino, mkfile(m + n, md, # links(ino, dirs), content)][mkinode(ino, md, false, # links(ino, dirs), 0, m + n).ino].meta = files0[ino, mkfile(m + n, md, m0, content0)][mkinode(ino, md, false, # links(ino, dirs), 0, m + n).ino].meta ∧ files1[ino, mkfile(m + n, md, # links(ino, dirs), content)] -- mkinode(ino, md, false, # links(ino, dirs), 0, m + n).ino = files0[ino, mkfile(m + n, md, m0, content0)] -- mkinode(ino, md, false, # links(ino, dirs), 0, m + n).ino ∧ 0 + n ≤ n1 ∧ n1 - 0 ≤ # buf ∧ write-inv (0, n1, buf, n, files0[ino, mkfile(m + n, md, m0, content0)][mkinode(ino, md, false, # links(ino, dirs), 0, m + n).ino].content, files1[ino, mkfile(m + n, md, # links(ino, dirs), content)][mkinode(ino, md, false, # links(ino, dirs), 0, m + n).ino].content)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ m - 0 = m; (s)% ⊦ n + 0 = n; (s)%ino ∈ files ⊦ files[ino, af] -- ino = files -- ino; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)