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Proof step 114 from proof truncate-empty (previous step)

files0[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n0 ≠ 0, n0 < VFS_PAGE_SIZE, afs-cons(dirs, files0), ino0 ∈ files0, ¬ m0 ∈ content0 ⊦ [asynced := ?] ((σ⊥ to VFS_PAGE_SIZE) + σ⊥ from n0 = σ⊥)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 115:
⊦ σ = σ2 ↔ # σ = # σ2 ∧ (∀ n. ⌜n⌝ < # σ → σ[n] = σ2[n])
Proof step 116:
files0[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n0 < VFS_PAGE_SIZE, afs-cons(dirs, files0), ino0 ∈ files0 ⊦ [asynced := ?] ( #((σ⊥ to VFS_PAGE_SIZE) + σ⊥ from n0) = # σ⊥ ∧ (∀ n. ⌜n⌝ < #((σ⊥ to VFS_PAGE_SIZE) + σ⊥ from n0) → ((σ⊥ to VFS_PAGE_SIZE) + σ⊥ from n0)[n] = (σ⊥)[n])), n0 = 0, m0 ∈ content0

Rule argument

spec: stream, inst: buffer-inf name: extensionality seq: ⊦ σ = σ2 ↔ # σ = # σ2 ∧ (∀ n. ⌜n⌝ < # σ → σ[n] = σ2[n]) subst: [σ2, σ] → [σ⊥, (σ⊥ to VFS_PAGE_SIZE) + σ⊥ from n0] flags: <all paths>

Additional information

Used terms: σ⊥, (σ⊥ to VFS_PAGE_SIZE) + σ⊥ from n0