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

files0[ino] = mkfile(m0, md0, n2, content0), files1[ino] = mkfile(m1, md1, n3, content1), content0.stream from m0 = σ⊥, write-inv(n0, n1, mkinode(ino, md, false, m, m3, m2), buf, n, dirs, files0, files1) ⊦ splice(buf, 0, (content0.stream to m0).buf, n0, n) = (content1.stream to (n ≠ 0 ∧ m0 < n0 + n ⊃ n0 + n;m0)).buf

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ files0[ino] = mkfile(m0, md0, n2, content0) ∧ files1[ino] = mkfile(m1, md1, n3, content1) ∧ write-inv(n0, n1, mkinode(ino, md, false, m, n4, m2), buf, n, dirs, files0, files1) → m0 = m1 ∧ md0 = md1
Proof step 4:
⊦ write-inv(n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files0
Proof step 5:
⊦ write-inv(n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files1
Proof step 6:
⊦ write-inv(n0, n1, mkinode(ino, md, false, m, m1, m0), buf, n, dirs, files0, files1) → ino ∈ files0
Proof step 7:
files0[ino] = mkfile(m1, md1, n2, content0), files1[ino] = mkfile(m1, md1, n3, content1), content0.stream from m1 = σ⊥, write-inv(n0, n1, mkinode(ino, md, false, m, m3, m2), buf, n, dirs, files0, files1), ino ∈ files1 ⊦ splice(buf, 0, (content0.stream to m1).buf, n0, n) = (content1.stream to (n ≠ 0 ∧ m1 < n0 + n ⊃ n0 + n;m1)).buf

Rule argument

Additional information

Used simplifier rules: write-inv-meta: ⊦ files0[ino] = mkfile(m0, md0, n2, content0) ∧ files1[ino] = mkfile(m1, md1, n3, content1) ∧ write-inv (n0, n1, mkinode(ino, md, false, m, n4, m2), buf, n, dirs, files0, files1) → m0 = m1 ∧ md0 = md1;%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;