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Proof step 111 from proof truncate-inv (previous step)

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 upto (m2 * VFS_PAGE_SIZE + n0))]), files2 ~ files2[ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0 upto (m2 * VFS_PAGE_SIZE + n0))], ino4 ∈ files2 ⊦ ((content0.stream to VFS_PAGE_SIZE * m2) + (σ⊥ to VFS_PAGE_SIZE)) + σ⊥ from m2 * VFS_PAGE_SIZE + n0 = σ⊥, n0 = 0, m2 ∈ content0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 112:
⊦ m ≤ n ∧ ¬ # σ1 < ⌜n⌝ → (σ1 to n) + σ2 from m = ((σ1 from m) to (n - m)) + σ2
Proof step 113:
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 upto (m2 * VFS_PAGE_SIZE + n0))]), afs-cons(dirs0, files2), files2 ~ files2[ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0 upto (m2 * VFS_PAGE_SIZE + n0))], ino4 ∈ files2 ⊦ ((content0.stream to VFS_PAGE_SIZE * m2) + (σ⊥ to VFS_PAGE_SIZE)) + σ⊥ from m2 * VFS_PAGE_SIZE + n0 = σ⊥, n0 = 0, m2 ∈ content0, m2 * VFS_PAGE_SIZE + n0 ≤ VFS_PAGE_SIZE * m2 ∧ ¬ # content0.stream < ⌜VFS_PAGE_SIZE * m2⌝

Rule argument

spec: stream, inst: buffer-inf name: swap-to-from-app seq: ⊦ m ≤ n ∧ ¬ # σ1 < ⌜n⌝ → (σ1 to n) + σ2 from m = ((σ1 from m) to (n - m)) + σ2 subst: [m, σ2, n, σ1] → [m2 * VFS_PAGE_SIZE + n0, (σ⊥ to VFS_PAGE_SIZE) + σ⊥, VFS_PAGE_SIZE * m2, content0.stream] flags: <all paths>

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%finp(σ1) ⊦ σ2 + σ1 = σ1 ↔ σ2 = []; (s)%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf] Used terms: m2 * VFS_PAGE_SIZE + n0, (σ⊥ to VFS_PAGE_SIZE) + σ⊥, VFS_PAGE_SIZE * m2, content0.stream