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Proof step 22 from proof emptystream-cancel (previous step)

# σ = ⌜n⌝ , (σ + ⌜λ n. zero⌝ )[n0] = zero, n0 < n ⊦ σ[n0] = zero

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ0[m]

Rule argument

spec: stream, inst: buffer-inf name: get-append-ls seq: ⊦ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ0[m] subst: [m, σ2, σ0] → [n0, ⌜λ n. zero⌝ , σ] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ2[m - (# σ0).n]; (s)% ⊦ ⌜nf0⌝ [n] = nf0(n); (s)%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]% ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: n0, ⌜λ n. zero⌝ , σ