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Proof step 2 from proof to-to-eq (previous step)

⊦ σ to n to n = σ to n, # σ < ⌜n⌝

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
¬ # σ < ⌜n⌝ ⊦ m ≤ n → σ to n to m = σ to m

Rule argument

spec: inst: name: to-to-leq seq: ¬ # σ < ⌜n⌝ ⊦ m ≤ n → σ to n to m = σ to m subst: [σ, n, m] → [σ, n, n] flags: current, []

Additional information

Used simplifier rules: ler: ⊦ m ≤ m; from specification nat Used terms: σ, n, n