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Proof step 36 from proof read-loop-inv (previous step)

# buf2 = # buf1, VFS_PAGE_SIZE = n4 + (n0 + n3) % VFS_PAGE_SIZE, files[m] = mkfile(n1 + n0 + n3, md0, # links(m, dirs), content), n3 < # buf1, afs-cons(dirs, files), read-inv(n0, n5 + n0 + n3, buf2, buf1, n3, content), read-inv(n0, n5 + n0 + n3, mkinode(m, md, boolvar, m0, m1, n1 + n0 + n3), buf2, buf3, n2, dirs, files), m ∈ files, min(n5, n4, n1) ≤ n5, (n0 + n3) % VFS_PAGE_SIZE + min(n5, n4, n1) ≤ VFS_PAGE_SIZE, n3 + min(n5, n4, n1) ≤ # buf1, n5 + n3 ≤ # buf1, min(n5, n4, n1) ≤ n1 ⊦ n1 = 0, n4 = 0, n5 = 0, read-inv (n0, n5 + n0 + n3, buf2, copy(getpage((n0 + n3) / VFS_PAGE_SIZE, content), (n0 + n3) % VFS_PAGE_SIZE, buf1, n3, min(n5, n4, n1)), n3 + min(n5, n4, n1), content)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
afs-cons(dirs, files), ino ∈ files, files[ino] = mkfile(n1 + n0 + n, md, m0, content), VFS_PAGE_SIZE = n2 + (n0 + n) % VFS_PAGE_SIZE, n3 + n ≤ # buf0, # buf0 = # buf1 ⊦ read-inv(n0, n3 + n0 + n, buf0, buf1, n, content) → read-inv (n0, n3 + n0 + n, buf0, copy(getpage((n0 + n) / VFS_PAGE_SIZE, content), (n0 + n) % VFS_PAGE_SIZE, buf1, n, min(n3, n2, n1)), min(n3, n2, n1) + n, content)

Rule argument

spec: <toplevel> name: read-inv-rec seq: afs-cons(dirs, files), ino ∈ files, files[ino] = mkfile(n1 + n0 + n, md, m0, content), VFS_PAGE_SIZE = n2 + (n0 + n) % VFS_PAGE_SIZE, n3 + n ≤ # buf0, # buf0 = # buf1 ⊦ read-inv(n0, n3 + n0 + n, buf0, buf1, n, content) → read-inv (n0, n3 + n0 + n, buf0, copy (getpage((n0 + n) / VFS_PAGE_SIZE, content), (n0 + n) % VFS_PAGE_SIZE, buf1, n, min(n3, n2, n1)), min(n3, n2, n1) + n, content) subst: [dirs, files, ino, md, m0, n1, n2, buf1, content, buf0, n, n3, n0] → [dirs, files, m, md0, # links(m, dirs), n1, n4, buf1, content, buf2, n3, n5, n0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s)% ⊦ ¬ n < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: dirs, files, m, md0, # links(m, dirs), n1, n4, buf1, content, buf2, n3, n5, n0