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Proof step 5 from proof write-inv-strong-rec (previous step)

files1[ino] = mkfile(m2, md0, m3, content), write-inv(n0, n1, mkinode(ino, md, boolvar, m0, m4, m1), buf, n, dirs, files0, files1), ino ∈ files1, (n0 + n) % VFS_PAGE_SIZE + min(n1 - n0 + n, n2) ≤ VFS_PAGE_SIZE ⊦ afs-cons (dirs, files1 [ino, mkfile (files0[ino].size, files0[ino].meta, m3, content[(n0 + n) / VFS_PAGE_SIZE, copy(buf, n, getpage((n0 + n) / VFS_PAGE_SIZE, content), (n0 + n) % VFS_PAGE_SIZE, min(n1 - n0 + n, n2))]) ]) ∧ ino ∈ files0 ∧ files0[ino].size = m1 ∧ m2 = files0[ino].size ∧ md0 = files0[ino].meta ∧ files1 -- ino = files0 -- ino ∧ n0 + n + min(n1 - n0 + n, n2) ≤ n1 ∧ n1 ≤ # buf + n0 ∧ write-inv (n0, n1, buf, n + min(n1 - n0 + n, n2), files0[ino].content, content[(n0 + n) / VFS_PAGE_SIZE, copy(buf, n, getpage((n0 + n) / VFS_PAGE_SIZE, content), (n0 + n) % VFS_PAGE_SIZE, min(n1 - n0 + n, n2))])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
files1[ino] = mkfile(m2, md0, m3, content), files0[ino] = mkfile(m, md1, m5, content0), write-inv(n0, n1, mkinode(ino, md, boolvar, m0, m4, m1), buf, n, dirs, files0, files1), ino ∈ files1, (n0 + n) % VFS_PAGE_SIZE + min(n1 - n0 + n, n2) ≤ VFS_PAGE_SIZE ⊦ afs-cons (dirs, files1 [ino, mkfile (m, md1, m3, content[(n0 + n) / VFS_PAGE_SIZE, copy(buf, n, getpage((n0 + n) / VFS_PAGE_SIZE, content), (n0 + n) % VFS_PAGE_SIZE, min(n1 - n0 + n, n2))]) ]) ∧ ino ∈ files0 ∧ m = m1 ∧ m2 = m ∧ md0 = md1 ∧ files1 -- ino = files0 -- ino ∧ n0 + n + min(n1 - n0 + n, n2) ≤ n1 ∧ n1 ≤ # buf + n0 ∧ write-inv (n0, n1, buf, n + min(n1 - n0 + n, n2), content0, content[(n0 + n) / VFS_PAGE_SIZE, copy(buf, n, getpage((n0 + n) / VFS_PAGE_SIZE, content), (n0 + n) % VFS_PAGE_SIZE, min(n1 - n0 + n, n2))])

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] → [files0[ino], m, md1, m4, 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: files0[ino], m, md1, m4, content0