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Proof step 2 from proof elim-fromto (previous step)

⊦ σ0 = σ to n ∧ σ1 = σ from n ↔ σ = σ0 + σ1 ∧ # σ0 = ⌜n⌝ , # σ < ⌜n⌝

User applied rule structural induction

And obtained the following new goals

Proof step 3:
⊦ σ0 = ⌜x⌝ to n ∧ σ1 = ⌜x⌝ from n ↔ ⌜x⌝ = σ0 + σ1 ∧ # σ0 = ⌜n⌝ , # ⌜x⌝ < ⌜n⌝
Proof step 7:
⊦ σ0 = ⌜nf⌝ to n ∧ σ1 = ⌜nf⌝ from n ↔ ⌜nf⌝ = σ0 + σ1 ∧ # σ0 = ⌜n⌝ , # ⌜nf⌝ < ⌜n⌝

Rule argument

indvar: σ

Additional information

Used simplifier rules: stream freely generated by ⌜ ⌝, ⌜ ⌝;;