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Proof step 55 from proof truncate-same-iso (previous step)

VFS_PAGE_SIZE = n0 + n1, files0[ino0] = mkfile(m, md, # links(ino0, dirs), content), m = m0 * VFS_PAGE_SIZE + n1, n1 < VFS_PAGE_SIZE, afs-cons(dirs, files0), ino0 ∈ files0, m0 ∈ content ⊦ VFS_PAGE_SIZE = 0, n1 = 0, content.stream to m = (content.stream to m0 * VFS_PAGE_SIZE) + (((content.stream from m0 * VFS_PAGE_SIZE) to VFS_PAGE_SIZE to n1) + (σ⊥ to n0)) + (content.stream from VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) to m

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 56:
VFS_PAGE_SIZE = n0 + n1, files0[ino0] = mkfile(m0 * VFS_PAGE_SIZE + n1, md, # links(ino0, dirs), content), n1 < VFS_PAGE_SIZE, afs-cons(dirs, files0), ino0 ∈ files0, m0 ∈ content ⊦ n0 = 0, n1 = 0, content.stream to m0 * VFS_PAGE_SIZE + n1 = (content.stream to m0 * VFS_PAGE_SIZE) + ((content.stream from m0 * VFS_PAGE_SIZE) to n1) + (σ⊥ to n0) + (content.stream from VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) to m0 * VFS_PAGE_SIZE + n1

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < m + n ↔ n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ VFS_PAGE_SIZE ≠ 0; (s)%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]%¬ # σ0 < ⌜n⌝ ⊦ m < n → σ0 to n to m = σ0 to m; (s)% ⊦ ¬ ∞ < n∞; (s)% ⊦ #(content.stream from n) = ∞; (s)