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Proof step 27 from proof read-inv-rec (previous step)

# buf1 = n4 + n + min(n3, n2, n1), # buf0 = # buf1, n0 + n = m0 * VFS_PAGE_SIZE + n5, VFS_PAGE_SIZE = n2 + n5, files[ino] = mkfile(n1 + n0 + n, md, # links(ino, dirs), content), n5 < VFS_PAGE_SIZE, afs-cons(dirs, files), ino ∈ files, min(n3, n2, n1) + n ≤ # buf1, n3 + n ≤ # buf1, n + min(n3, n2, n1) ≤ # buf1, n5 + min(n3, n2, n1) ≤ VFS_PAGE_SIZE ⊦ (((content.stream from n0) to n) + (⌜buf0⌝ from n) to n) + ((content.stream from m0 * VFS_PAGE_SIZE from n5) to (VFS_PAGE_SIZE - n5) to min(n3, n2, n1)) + (⌜buf0⌝ from n + min(n3, n2, n1)) = ((content.stream from n0) to min(n3, n2, n1) + n) + (⌜buf0⌝ from min(n3, n2, n1) + n), n2 = 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 28:
# buf0 = # buf1, # buf1 = n4 + n + min(n3, n2, n1), n0 + n = m0 * VFS_PAGE_SIZE + n5, VFS_PAGE_SIZE = n2 + n5, VFS_PAGE_SIZE = n6 + n5, files[ino] = mkfile(n1 + n0 + n, md, # links(ino, dirs), content), n5 < VFS_PAGE_SIZE, afs-cons(dirs, files), ino ∈ files, n5 + min(n3, n2, n1) ≤ VFS_PAGE_SIZE, n + min(n3, n2, n1) ≤ # buf1, n3 + n ≤ # buf1, min(n3, n2, n1) + n ≤ # buf1, n5 ≤ VFS_PAGE_SIZE ⊦ (((content.stream from n0) to n) + (⌜buf0⌝ from n) to n) + ((content.stream from m0 * VFS_PAGE_SIZE from n5) to n6 to min(n3, n2, n1)) + (⌜buf0⌝ from n + min(n3, n2, n1)) = ((content.stream from n0) to min(n3, n2, n1) + n) + (⌜buf0⌝ from min(n3, n2, n1) + n), n2 = 0

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [VFS_PAGE_SIZE, n5, n6]

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: VFS_PAGE_SIZE, n5, n6