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Proof step 107 from proof truncate-greater (previous step)

m1 * VFS_PAGE_SIZE + n1 = m1 * VFS_PAGE_SIZE + n1, files1[m0] = mkfile(m, md0, # links(m0, dirs), content0), n1 < VFS_PAGE_SIZE, afs-cons(dirs, files1), m0 ∈ files1 ⊦ [asynced := ?] ((content0.stream to (m1 + 1) * VFS_PAGE_SIZE) + σ⊥ to n0 + m1 * VFS_PAGE_SIZE + n1 = (content0.stream to m1 * VFS_PAGE_SIZE + n1) + (σ⊥ to n0)), n0 = 0, n1 = 0, n1 ≠ 0 ∧ m1 ∈ content0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 108:
files1[m0] = mkfile(m, md0, # links(m0, dirs), content0), n0 ≠ 0, n1 ≠ 0, n1 < VFS_PAGE_SIZE, afs-cons(dirs, files1), m0 ∈ files1, ¬ m1 ∈ content0 ⊦ [asynced := ?] ( ((content0.stream to VFS_PAGE_SIZE * m1) + (σ⊥ to VFS_PAGE_SIZE)) + σ⊥ to n0 + m1 * VFS_PAGE_SIZE + n1 = (content0.stream to m1 * VFS_PAGE_SIZE) + (σ⊥ to n1 + n0))

Rule argument

Additional information

Used simplifier rules: ⊦ (σ⊥ to n) + (σ⊥ to m) = σ⊥ to n + m; (s)%⊦ ¬ m ∈ content ∧ n < VFS_PAGE_SIZE → content.stream to m * VFS_PAGE_SIZE + n = (content.stream to m * VFS_PAGE_SIZE) + (σ⊥ to n); (s)%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]%⊦ ¬ m ∈ content → content.stream to m * VFS_PAGE_SIZE + VFS_PAGE_SIZE = (content.stream to m * VFS_PAGE_SIZE) + (σ⊥ to VFS_PAGE_SIZE); (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m * (n + 1) = m * n + m; (s)