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Proof step 10 from proof write-inv-stream (previous step)

files1 -- ino = files0 -- ino, files0[ino] = mkfile(m1, md1, n2, content0), files1[ino] = mkfile(m1, md1, # links(ino, dirs), content1), afs-cons(dirs, files1), write-inv(n0, n1, buf, n, content0, content1), ino ∈ files0, ino ∈ files1, n0 + n ≤ n1, n1 ≤ # buf + n0, n ≤ # buf ⊦ content1.stream = (content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ write-inv(n0, n1, buf, n, content0, content1) ↔ content1.stream = (content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n)

Rule argument

spec: <toplevel> name: write-inv seq: ⊦ write-inv(n0, n1, buf, n, content0, content1) ↔ content1.stream = (content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n) subst: [content1, content0, n, buf, n1, n0] → [content1, content0, n, buf, n1, n0] flags: <all paths>

Additional information

Used simplifier rules: append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf] Used terms: content1, content0, n, buf, n1, n0