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Proof step 2 from proof write-inv-ls (previous step)

write-inv(n0, n0 + n1, mkinode(ino, md, false, m, m1, m0), buf, n2, dirs, files0, files1) ⊦ n2 ≤ n1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ write-inv(n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files0
Proof step 4:
⊦ write-inv(n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files1
Proof step 5:
⊦ write-inv(n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files0
Proof step 6:
n1 < n2, write-inv(n0, n0 + n1, mkinode(ino, md, false, m, m1, m0), buf, n2, dirs, files0, files1), ino ∈ files1 ⊦

Rule argument

Additional information

Used simplifier rules: write-inv-in1: ⊦ write-inv (n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files0;%write-inv-in0: ⊦ write-inv (n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files1;%write-inv-in1: ⊦ write-inv (n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files0;% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)