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

files1[ino] = mkfile(m1, md1, n3, content1), files0[ino] = mkfile(m0, md0, n2, content0), write-inv(n0, n1, mkinode(ino, md, false, m, m3, m2), buf, n, dirs, files0, files1) ⊦ content1.stream = (content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n)

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:
files1[ino] = mkfile(m1, md1, n3, content1), files0[ino] = mkfile(m1, md1, n2, content0), write-inv(n0, n1, mkinode(ino, md, false, m, m3, m2), buf, n, dirs, files0, files1), ino ∈ files1 ⊦ content1.stream = (content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n)

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;