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Proof step 106 from proof truncate-inv (previous step)

VFS_PAGE_SIZE = n2 + n0, files2[ino4] = mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0), n0 < VFS_PAGE_SIZE, afs-cons (dirs0, files2 [ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0[m2, fill(content0[m2], zero, n0, n2)] upto (m2 * VFS_PAGE_SIZE + n0)) ]), afs-cons(dirs0, files2), files2 ~ files2 [ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0[m2, fill(content0[m2], zero, n0, n2)] upto (m2 * VFS_PAGE_SIZE + n0)) ], m2 ∈ content0, ino4 ∈ files2 ⊦ (σ⊥ to n2 to n2) + σ⊥ = σ⊥, n0 = 0, n2 = 0, #(σ⊥ to n2) < ⌜n2⌝

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 107:
VFS_PAGE_SIZE = n2 + n0, files2[ino4] = mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0), n0 < VFS_PAGE_SIZE, afs-cons(dirs0, files2), afs-cons (dirs0, files2 [ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0[m2, fill(content0[m2], zero, n0, n2)] upto (m2 * VFS_PAGE_SIZE + n0)) ]), files2 ~ files2 [ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0[m2, fill(content0[m2], zero, n0, n2)] upto (m2 * VFS_PAGE_SIZE + n0)) ], ino4 ∈ files2, m2 ∈ content0 ⊦ (σ⊥ to n2) + σ⊥ = σ⊥, n0 = 0, n2 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)%¬ # σ0 < ⌜n⌝ ⊦ σ0 to n to n = σ0 to n; (s)% ⊦ ¬ ∞ < n∞; (s)% ⊦ # σ⊥ = ∞; (s)