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Proof step 101 from proof infinite-append-butlast (previous step)

(σ to # y) + ⌜σ[# y] '⌝ = ⌜y⌝ + ⌜a '⌝ , lf(1) = a ' + x0, ii(1) = # y + 1, ii(0) = 0, a ∈ lf(1), ⌜# y⌝ < # σ, (finp(σ) ⊃ # σ = ⌜ii(n)⌝ ∧ (∀ m. n ≤ m → (m = 0 ⊃ y + a ';lf(m).rest) = [] ∧ ii(m) = ii(n));∀ n. ∃ m. ii(m) ≤ n ∧ n < ii(m + 1)), ∀ n. lf(n).last = lf(n + 1).first ∧ lf(n) ≠ [], ∀ m, n. m ≤ n → ii(m) ≤ ii(n), ∀ n. ii(n + 1) = ii(n) + # (n = 0 ⊃ y + a ';lf(n).rest) ∧ ¬ # σ < ⌜ii(n + 1)⌝ ∧ (σ from ii(n)) to # (n = 0 ⊃ y + a ';lf(n).rest) = ⌜(n = 0 ⊃ y + a ';lf(n).rest)⌝ , ∀ n. n ≠ 0 → ii(n) ≠ 0 ⊦ lf(1) = [], σ[# y] = a

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: stream inst: name: append-split seq: ⊦ finp(σ) ∧ # σ = # σ1 → (σ + σ0 = σ1 + σ2 ↔ σ = σ1 ∧ σ0 = σ2) subst: [σ2, σ1, σ0, σ] → [⌜a '⌝ , ⌜y⌝ , ⌜σ[# y] '⌝ , σ to # y] flags: rewrite

Additional information

Used simplifier rules: ls-le: ⊦ n∞ < n∞0 → ¬ n∞0 < n∞; from specification nat-inf%size-to: ¬ # σ < ⌜n⌝ ⊦ #(σ to n) = ⌜n⌝ ; from specification stream%size-fin: ⊦ # ⌜x⌝ = ⌜# x⌝ ; from specification stream%inj: ⊦ ⌜m⌝ = ⌜m0⌝ ↔ m = m0; from specification nat-inf-basic%inj-02: ⊦ ⌜x⌝ = ⌜x0⌝ ↔ x = x0; from specification stream-basic%c-04: ⊦ a ' = b ' ↔ a = b; from specification list%fin-to: ⊦ finp(σ to m); from specification stream Used terms: ⌜a '⌝ , ⌜y⌝ , ⌜σ[# y] '⌝ , σ to # y