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Proof step 58 from proof read-inv-rec (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 59:
# buf1 = n4 + n + min(n3, n6, n1), # buf0 = # buf1, n0 + n = m0 * VFS_PAGE_SIZE + n5, VFS_PAGE_SIZE = n6 + n5, files[ino] = mkfile(n1 + n0 + n, md, # links(ino, dirs), content), n2 = n7 + n, n < # buf1, n2 < # buf1, n2 < n + min(n3, n6, n1), ⌜n2⌝ < ⌜n⌝ + ⌜min(n3, n6, n1)⌝ + #(⌜buf0⌝ from n + min(n3, n6, n1)), n5 < VFS_PAGE_SIZE, afs-cons(dirs, files), ino ∈ files, n ≤ n2, min(n3, n6, n1) + n ≤ # buf1, n3 + n ≤ # buf1, n + min(n3, n6, n1) ≤ # buf1, n5 + min(n3, n6, n1) ≤ VFS_PAGE_SIZE, min(n3, n6, n1) ≤ n6 ⊦ n4 + min(n3, n6, n1) = 0, (((content.stream from n0 + n) to min(n3, n6, n1)) + (⌜buf0⌝ from n + min(n3, n6, n1)))[n7] = getbyte(n0 + n2, content), n1 = 0, n3 = 0, n6 = 0

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n2, n, n7]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n2, n, n7