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Proof step 24 from proof monls-mon-implies-monls (previous step)

(lim(nσf) to n + 2) + nσ = nσf(n0), ⌜n⌝ + ⌜1⌝ < # lim(nσf), # nσf(n0) < # lim(nσf), mon(nσf), lim(nσf)[n + 1] ≤ lim(nσf)[n], ∀ 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: ⊦ #(nσ + nσ0) = # nσ + # nσ0; (s)% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%¬ # nσ < ⌜n⌝ ⊦ #(nσ to n) = ⌜n⌝ ; (s)%append-assoc: ⊦ (nσ + nσ0) + nσ1 = nσ + nσ0 + nσ1; from specification stream[natstream]% ⊦ ⌜n⌝ + n∞1 < ⌜n⌝ + n∞2 ↔ n∞1 < n∞2; (s)% ⊦ ⌜1⌝ < n∞ ↔ n∞ ≠ ⌜0⌝ ∧ n∞ ≠ ⌜1⌝ ; (s)% ⊦ n < m → (⌜(* n)⌝ = ⌜(* m)⌝ + n∞2 ↔ false); (s)%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