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Proof step 4 from proof swap-inf-to-from-app (previous step)

⊦ ⌜nf to n0 + m⌝ + σ0 from m = ⌜(nf from m) to n0⌝ + σ0

User applied rule insert lemma

And obtained the following new goals

Proof step 5:
⊦ m ≤ n ∧ ¬ # σ < ⌜n⌝ → (σ to n) + σ0 from m = ((σ from m) to (n - m)) + σ0

Rule argument

spec: inst: name: swap-to-from-app seq: ⊦ m ≤ n ∧ ¬ # σ < ⌜n⌝ → (σ to n) + σ0 from m = ((σ from m) to (n - m)) + σ0 subst: [m, n, σ, σ0] → [m, m + n0, ⌜nf⌝ , σ0] flags: current, []

Additional information

Used simplifier rules: size-inf: ⊦ # ⌜nf⌝ = ∞;%to-inf: ⊦ ⌜nf⌝ to n = ⌜nf to n⌝ ;%from-inf: ⊦ ⌜nf⌝ from n = ⌜nf from n⌝ ;%lep: ⊦ m ≤ m + n; from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%add-fin: ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; from specification nat-inf%less-inf1: ⊦ ¬ ∞ < n∞; from specification nat-inf%eq-01: ⊦ m + n - m = n; from specification nat Used terms: m, m + n0, ⌜nf⌝ , σ0