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

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

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, n0 + n1, mkinode(ino, md, false, m, m1, m0), buf, n2, dirs, files0, files1) → n2 ≤ n1
Proof step 6:
⊦ write-inv(n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files0
Proof step 7:
⊦ write-inv(n0, n0 + n1, mkinode(ino, md, false, m, m1, m0), buf, n2, dirs, files0, files1) → n2 ≤ n1
Proof step 8:
write-inv(n0, n0 + n1, mkinode(ino, md, false, m, m1, m0), buf, n2, dirs, files0, files1), ino ∈ files1 ⊦ files0 -- ino = files1 -- ino

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-ls: ⊦ write-inv (n0, n0 + n1, mkinode(ino, md, false, m, m1, m0), buf, n2, dirs, files0, files1) → n2 ≤ n1;%write-inv-in1: ⊦ write-inv (n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files0;%write-inv-ls: ⊦ write-inv (n0, n0 + n1, mkinode(ino, md, false, m, m1, m0), buf, n2, dirs, files0, files1) → n2 ≤ n1;%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic