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Proof step 23 from proof monls-mon-implies-monls (previous step)

(lim(nσf) to n + 2) + nσ = nσf(n0), ⌜n⌝ + ⌜1⌝ < # lim(nσf), mon(nσf), lim(nσf)[n + 1] ≤ lim(nσf)[n], # nσf(n0) < # lim(nσf), ∀ n. nσf(n) ⊑ lim(nσf) ⊦ ⌜n⌝ + ⌜1⌝ < # nσf(n0), # lim(nσf) < ⌜n⌝ + ⌜2⌝

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 1 flags: rotate, discard

Additional information

Used simplifier rules: size-append: ⊦ #(nσ + nσ0) = # nσ + # nσ0; from specification stream[natstream]%add-fin: ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; from specification nat-inf%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%size-to: ¬ # nσ < ⌜n⌝ ⊦ #(nσ to n) = ⌜n⌝ ; from specification stream[natstream]%append-assoc: ⊦ (nσ + nσ0) + nσ1 = nσ + nσ0 + nσ1; from specification stream[natstream]%add-ls-cancel-num-04: ⊦ m ≤ n → (⌜(* m)⌝ + n∞2 < ⌜(* n)⌝ + n∞1 ↔ n∞2 < ⌜n - m⌝ + n∞1); from specification nat-inf%less-succ-leq: ⊦ ⌜n⌝ < ⌜1⌝ + n∞ ↔ ¬ n∞ < ⌜n⌝ ; from specification nat-inf%add-not-less: ⊦ ¬ n∞ + n∞1 < n∞1; from specification nat-inf%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf