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Proof step 30 from proof writepage-prepost (previous step)

⌜buf0⌝ = (σ from n3 * VFS_PAGE_SIZE) to VFS_PAGE_SIZE, ((m0 =>mkfile(n2, md, m1, (σ to n3 * VFS_PAGE_SIZE) + ⌜copy(buf1, m, buf0, n0, n1)⌝ + (σ from VFS_PAGE_SIZE * n3 + VFS_PAGE_SIZE)) * F))(files0), ((m0 =>mkfile(n2, md, m1, σ) * F))(files), afs-cons(dirs, files), m0 ∈ files, n0 + n1 ≤ # buf0, m + n1 ≤ # buf1, n0 + n1 ≤ VFS_PAGE_SIZE ⊦ ((m0 =>mkfile(n2, md, m1, (σ to n3 * VFS_PAGE_SIZE + n0) + ((⌜buf1⌝ from m) to n1) + (σ from n3 * VFS_PAGE_SIZE + n0 + n1)) * F))(files0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ ((ino =>mkfile(n, md, m, σ0) * F))(files) → (((ino =>mkfile(n, md, m, σ1) * F))(files) ↔ σ0 = σ1)
Proof step 32:
⌜buf0⌝ = (σ from n3 * VFS_PAGE_SIZE) to VFS_PAGE_SIZE, ((m0 =>mkfile(n2, md, m1, σ) * F))(files), ((m0 =>mkfile(n2, md, m1, (σ to n3 * VFS_PAGE_SIZE) + ⌜copy(buf1, m, buf0, n0, n1)⌝ + (σ from VFS_PAGE_SIZE * n3 + VFS_PAGE_SIZE)) * F))(files0), afs-cons(dirs, files), m0 ∈ files, n0 + n1 ≤ VFS_PAGE_SIZE, m + n1 ≤ # buf1, n0 + n1 ≤ # buf0 ⊦ (σ to n3 * VFS_PAGE_SIZE) + ⌜copy(buf1, m, buf0, n0, n1)⌝ + (σ from VFS_PAGE_SIZE * n3 + VFS_PAGE_SIZE) = (σ to n3 * VFS_PAGE_SIZE + n0) + ((⌜buf1⌝ from m) to n1) + (σ from n3 * VFS_PAGE_SIZE + n0 + n1)

Rule argument

spec: afs-contracts name: mkfile-stream-reduce seq: ⊦ ((ino =>mkfile(n, md, m, σ0) * F))(files) → (((ino =>mkfile(n, md, m, σ1) * F))(files) ↔ σ0 = σ1) subst: [σ0, files, F, σ1, m, md, n, ino] → [ (σ to n3 * VFS_PAGE_SIZE) + ⌜copy(buf1, m, buf0, n0, n1)⌝ + (σ from VFS_PAGE_SIZE * n3 + VFS_PAGE_SIZE), files0, F, (σ to n3 * VFS_PAGE_SIZE + n0) + ((⌜buf1⌝ from m) to n1) + (σ from n3 * VFS_PAGE_SIZE + n0 + n1), m1, md, n2, m0] flags: <all paths>

Additional information

Used simplifier rules: append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf] Used terms: (σ to n3 * VFS_PAGE_SIZE) + ⌜copy(buf1, m, buf0, n0, n1)⌝ + (σ from VFS_PAGE_SIZE * n3 + VFS_PAGE_SIZE), files0, F, (σ to n3 * VFS_PAGE_SIZE + n0) + ((⌜buf1⌝ from m) to n1) + (σ from n3 * VFS_PAGE_SIZE + n0 + n1), m1, md, n2, m0