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Proof step 36 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⊥, n3 < n1, m1 < n1, n3 < # buf + n0, m1 < # buf + n0, m1 < n0 + n, n3 < n0 + n, afs-cons(dirs, files1), ino ∈ files1, ino ∈ files0, n ≤ # buf, n1 ≤ # buf + n0, n0 + n ≤ n1 ⊦ (n3 < n0 ⊃ (m1 ≤ n3 ⊃ zero;getbyte(n3, content0));buf[n3 - n0]) = ((content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n))[n3], n = 0

User applied rule case distinction

And obtained the following new goals

Proof step 37:
files1 -- ino = files0 -- ino, files1[ino] = mkfile(m1, md1, # links(ino, dirs), content1), files0[ino] = mkfile(m1, md1, n2, content0), content0.stream from m1 = σ⊥, n3 < n0 + n, m1 < n0 + n, m1 < # buf + n0, n3 < # buf + n0, m1 < n1, n3 < n1, n3 < n0, afs-cons(dirs, files1), ino ∈ files0, ino ∈ files1, n0 + n ≤ n1, n1 ≤ # buf + n0, n ≤ # buf ⊦ (m1 ≤ n3 ⊃ zero;getbyte(n3, content0)) = ((content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n))[n3], n = 0
Proof step 51:
files1 -- ino = files0 -- ino, files1[ino] = mkfile(m1, md1, # links(ino, dirs), content1), files0[ino] = mkfile(m1, md1, n2, content0), content0.stream from m1 = σ⊥, n3 < n0 + n, m1 < n0 + n, m1 < # buf + n0, n3 < # buf + n0, m1 < n1, n3 < n1, afs-cons(dirs, files1), ino ∈ files0, ino ∈ files1, n0 + n ≤ n1, n1 ≤ # buf + n0, n ≤ # buf ⊦ buf[n3 - n0] = ((content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n))[n3], n = 0, n3 < n0

Rule argument

pos: right 1

Proof step 36 from proof write-inv-post (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information