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Proof step 75 from proof truncate-empty (previous step)

VFS_PAGE_SIZE = n2 + n1, files1[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n1 ≠ 0, n2 ≠ 0, n1 < VFS_PAGE_SIZE, afs-cons(dirs, files1), m0 ∈ content0, ino0 ∈ files1 ⊦ [asynced := ?] ((σ⊥ to n2) + σ⊥ = σ⊥)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 76:
⊦ # σ ≠ ∞ → (σ + σ⊥ = σ⊥ ↔ σ = σ⊥ to (# σ).n)

Rule argument

spec: buffer-inf-conv name: emptystream-cancel seq: ⊦ # σ ≠ ∞ → (σ + σ⊥ = σ⊥ ↔ σ = σ⊥ to (# σ).n) subst: [σ] → [σ⊥ to n2] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # σ⊥ = ∞; (s)% ⊦ ¬ ∞ < n∞; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ ⌜m⌝ ≠ ∞; (s)% ⊦ ⌜m⌝ .n = m; (s)% ⊦ ⌜m⌝ < ∞; (s) Used terms: σ⊥ to n2