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Proof step 32 from proof read-loop-inv (previous step)

# buf2 = # buf1, VFS_PAGE_SIZE = n4 + (n0 + n3) % VFS_PAGE_SIZE, files[m] = mkfile(m3, md0, # links(m, dirs), content), n0 + n3 < n1, n0 + n3 < m3, n3 < # buf1, afs-cons(dirs, files), read-inv(n0, n1, buf2, buf1, n3, content), read-inv(n0, n1, mkinode(m, md, boolvar, m0, m1, m3), buf2, buf3, n2, dirs, files), m ∈ files, n3 + min(n1 - n0 + n3, n4, m3 - n0 + n3) ≤ # buf1, n1 ≤ # buf1 + n0, (n0 + n3) % VFS_PAGE_SIZE + min(n1 - n0 + n3, n4, m3 - n0 + n3) ≤ VFS_PAGE_SIZE ⊦ m3 = n0 + n3, n1 = n0 + n3, n4 = 0, n0 + n3 + min(n1 - n0 + n3, n4, m3 - n0 + n3) ≤ n1 ∧ n0 + n3 + min(n1 - n0 + n3, n4, m3 - n0 + n3) ≤ m3 ∧ read-inv (n0, n1, buf2, copy(getpage((n0 + n3) / VFS_PAGE_SIZE, content), (n0 + n3) % VFS_PAGE_SIZE, buf1, n3, min(n1 - n0 + n3, n4, m3 - n0 + n3)), n3 + min(n1 - n0 + n3, n4, m3 - n0 + n3), content)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 33:
# buf2 = # buf1, VFS_PAGE_SIZE = n4 + (n0 + n3) % VFS_PAGE_SIZE, files[m] = mkfile(m3, md0, # links(m, dirs), content), n1 = n5 + n0 + n3, n3 < # buf1, n0 + n3 < m3, n0 + n3 < n1, afs-cons(dirs, files), read-inv(n0, n1, mkinode(m, md, boolvar, m0, m1, m3), buf2, buf3, n2, dirs, files), read-inv(n0, n1, buf2, buf1, n3, content), m ∈ files, (n0 + n3) % VFS_PAGE_SIZE + min(n5, n4, m3 - n0 + n3) ≤ VFS_PAGE_SIZE, n1 ≤ # buf1 + n0, n3 + min(n5, n4, m3 - n0 + n3) ≤ # buf1, n0 + n3 ≤ n1 ⊦ m3 = n0 + n3, n1 = n0 + n3, n4 = 0, n0 + n3 + min(n5, n4, m3 - n0 + n3) ≤ n1 ∧ n0 + n3 + min(n5, n4, m3 - n0 + n3) ≤ m3 ∧ read-inv (n0, n1, buf2, copy(getpage((n0 + n3) / VFS_PAGE_SIZE, content), (n0 + n3) % VFS_PAGE_SIZE, buf1, n3, min(n5, n4, m3 - n0 + n3)), n3 + min(n5, n4, m3 - n0 + n3), content)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [n0 + n3, n1, n]

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n0 + n3, n1, n