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Proof step 19 from proof read-inv-post (previous step)

# buf0 = # buf1, files[ino] = mkfile(m, md, # links(ino, dirs), content), buf1[n2] = (⌜buf0⌝ from n)[n2 - n], ⌜# buf1⌝ = ⌜n⌝ + #(⌜buf0⌝ from n), n2 < # buf1, n < # buf1, afs-cons(dirs, files), ino ∈ files, n0 + n ≤ n1, n0 + n ≤ m, n1 ≤ # buf1 + n0, n ≤ n2 ⊦ buf0[n2] = buf1[n2]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 20:
# buf0 = # buf1, buf1[n2] = (⌜buf0⌝ from n)[n3], files[ino] = mkfile(m, md, # links(ino, dirs), content), n2 = n3 + n, ⌜# buf1⌝ = ⌜n⌝ + #(⌜buf0⌝ from n), n < # buf1, n2 < # buf1, afs-cons(dirs, files), ino ∈ files, n ≤ n2, n1 ≤ # buf1 + n0, n0 + n ≤ m, n0 + n ≤ n1 ⊦ buf0[n2] = buf1[n2]

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n2, n, n3]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n2, n, n3