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Proof step 18 from proof write-inv-post (previous step)

files1 -- ino = files0 -- ino, files0[ino] = mkfile(m1, md1, n2, content0), files1[ino] = mkfile(m1, md1, # links(ino, dirs), content1), content0.stream from m1 = σ⊥, n = 0, afs-cons(dirs, files1), ino ∈ files1, ino ∈ files0, n ≤ # buf, n1 ≤ # buf + n0, n0 + n ≤ n1 ⊦ # splice(buf, 0, (content0.stream to m1).buf, n0, n) = (n ≠ 0 ∧ m1 < n0 + n ⊃ n0 + n;m1) ∧ ( n3 < # splice(buf, 0, (content0.stream to m1).buf, n0, n) → splice(buf, 0, (content0.stream to m1).buf, n0, n)[n3] = ((content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n))[n3])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
files1 -- ino = files0 -- ino, files0[ino] = mkfile(m1, md1, n2, content0), files1[ino] = mkfile(m1, md1, # links(ino, dirs), content1), content0.stream from m1 = σ⊥, n3 < m1, afs-cons(dirs, files1), ino ∈ files1, ino ∈ files0, n0 ≤ n1, n1 ≤ # buf + n0 ⊦ getbyte(n3, content0) = ((content0.stream to n0) + (content0.stream from n0))[n3]

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)% ⊦ m < n → n ≠ 0; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]% ⊦ [] + σ0 = σ0; (s)% ⊦ σ0 to 0 = []; (s)% ⊦ content.stream[n] = getbyte(n, content); (s)%m < n, ¬ # σ0 < ⌜n⌝ ⊦ (σ0 to n)[m] = σ0[m]; (s)%finp(σ), ⌜n⌝ < # σ ⊦ σ.buf[n] = σ[n]; (s)% ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s)% ⊦ ⌜m⌝ .n = m; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ ¬ ∞ < n∞; (s)% ⊦ # content.stream = ∞; (s)%finp(σ) ⊦ # σ.buf = (# σ).n; (s)% ⊦ finp(σ0 to m); (s)% ⊦ splice(buf, n0, buf0, n1, 0) = buf0; (s)% ⊦ 0 ≤ m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)