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Proof step 78 from proof write-inv-rec (previous step)

VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE = n3 + m0 * VFS_PAGE_SIZE + n2, n0 + n = m0 * VFS_PAGE_SIZE + n2, files1 -- ino = files0 -- ino, VFS_PAGE_SIZE = n4 + n2 + m, files1[ino] = mkfile(m2, md0, # links(ino, dirs), content0), files0[ino] = mkfile(m2, md0, m4, content), n2 < VFS_PAGE_SIZE, afs-cons(dirs, files1), ino ∈ files1, ino ∈ files0, n2 + m ≤ VFS_PAGE_SIZE, m0 * VFS_PAGE_SIZE ≤ n1, m0 * VFS_PAGE_SIZE ≤ m0 * VFS_PAGE_SIZE + n2, n + m ≤ # buf, n ≤ # buf, n1 ≤ # buf + n0, m0 * VFS_PAGE_SIZE + n2 ≤ n1, m + n2 ≤ VFS_PAGE_SIZE, m0 * VFS_PAGE_SIZE ≤ # buf + n0, m0 * VFS_PAGE_SIZE ≤ n3 + m0 * VFS_PAGE_SIZE + n2 ⊦ ((content.stream to n0) + (⌜buf⌝ to n) to m0 * VFS_PAGE_SIZE) + (((content.stream to n0) + (⌜buf⌝ to n) to m0 * VFS_PAGE_SIZE + n2) from m0 * VFS_PAGE_SIZE) + ((⌜buf⌝ from n) to m) + ((content.stream from (m0 * VFS_PAGE_SIZE + n2) + m) to n4) + (content.stream from (m0 * VFS_PAGE_SIZE + n2) + n3) = (content.stream to n0) + (⌜buf⌝ to n + m) + (content.stream from n0 + n + m), n4 + m = 0

User applied rule insert equation

And obtained the following new goals

Proof step 79:
n0 + n = m0 * (n4 + n2 + m) + n2, (n4 + n2 + m) * m0 + n4 + n2 + m = n3 + m0 * (n4 + n2 + m) + n2, files1 -- ino = files0 -- ino, VFS_PAGE_SIZE = n4 + n2 + m, files0[ino] = mkfile(m2, md0, m4, content), files1[ino] = mkfile(m2, md0, # links(ino, dirs), content0), n2 < n4 + n2 + m, afs-cons(dirs, files1), ino ∈ files0, ino ∈ files1, m0 * (n4 + n2 + m) ≤ n3 + m0 * (n4 + n2 + m) + n2, m0 * (n4 + n2 + m) ≤ # buf + n0, m + n2 ≤ n4 + n2 + m, m0 * (n4 + n2 + m) + n2 ≤ n1, n1 ≤ # buf + n0, n ≤ # buf, n + m ≤ # buf, m0 * (n4 + n2 + m) ≤ m0 * (n4 + n2 + m) + n2, m0 * (n4 + n2 + m) ≤ n1, n2 + m ≤ n4 + n2 + m ⊦ n4 + m = 0, ((content.stream to n0) + (⌜buf⌝ to n) to m0 * (n4 + n2 + m)) + (((content.stream to n0) + (⌜buf⌝ to n) to m0 * (n4 + n2 + m) + n2) from m0 * (n4 + n2 + m)) + ((⌜buf⌝ from n) to m) + ((content.stream from (m0 * (n4 + n2 + m) + n2) + m) to n4) + (content.stream from (m0 * (n4 + n2 + m) + n2) + n3) = (content.stream to n0) + (⌜buf⌝ to n + m) + (content.stream from n0 + n + m)

Rule argument

pos: left 4 flags:

Proof step 78 from proof write-inv-rec (previous step)

User applied rule insert equation

And obtained the following new goals

Rule argument

Additional information