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Proof step 122 from proof infinite-append-butlast (previous step)

lf(n1 + 1) = σ[m0] ' + x0, ii(n1 + 1) = m0 + 1, ii(0) = 0, ii(2 + n1) = (m0 + 1) + # x0, (σ from m0 + 1) to # x0 = ⌜x0⌝ , lf(2 + n1) = lf(n1 + 1).last ' + x1, σ[m0] ∈ lf(n1 + 1), lf(n1 + 1).last ∈ lf(2 + n1), ∀ n. n ≠ 0 → ii(n) ≠ 0, ∀ m, n. m ≤ n → ii(m) ≤ ii(n), (finp(σ) ⊃ # σ = ⌜ii(n)⌝ ∧ (∀ m. n ≤ m → (m = 0 ⊃ lf(0);lf(m).rest) = [] ∧ ii(m) = ii(n));∀ n. ∃ m. ii(m) ≤ n ∧ n < ii(m + 1)) ⊦ σ[m0 + # x0] = lf(n1 + 1).last, lf(n1 + 1) = [], # σ < ⌜m0⌝ + ⌜1⌝ + ⌜# x0⌝

User applied rule insert equation

And obtained the following new goals

Proof step 123:
ii(n1 + 1) = m0 + 1, ii(0) = 0, ii(2 + n1) = (m0 + 1) + # x0, (σ from m0 + 1) to # x0 = ⌜x0⌝ , lf(2 + n1) = (σ[m0] ' + x0).last ' + x1, σ[m0] ∈ σ[m0] ' + x0, (σ[m0] ' + x0).last ∈ lf(2 + n1), ∀ n. n ≠ 0 → ii(n) ≠ 0, ∀ m, n. m ≤ n → ii(m) ≤ ii(n), (finp(σ) ⊃ # σ = ⌜ii(n)⌝ ∧ (∀ m. n ≤ m → (m = 0 ⊃ lf(0);lf(m).rest) = [] ∧ ii(m) = ii(n));∀ n. ∃ m. ii(m) ≤ n ∧ n < ii(m + 1)) ⊦ σ[m0 + # x0] = (σ[m0] ' + x0).last, σ[m0] ' + x0 = [], # σ < ⌜m0⌝ + ⌜1⌝ + ⌜# x0⌝

Rule argument

pos: left 1 flags: discard

Proof step 122 from proof infinite-append-butlast (previous step)

User applied rule insert equation

And obtained the following new goals

Rule argument

Additional information