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Proof step 1 from proof finp-append-02 (conclusion)

⊦ finp(⌜x⌝ + σ) ↔ finp(σ)

User applied rule structural induction

And closed the goal!

Rule argument

indvar: σ

Additional information

Used simplifier rules: neq-fin-inf-03: ⊦ σ0 + ⌜x⌝ = ⌜nf0⌝ ↔ σ0 = ⌜nf0⌝ ;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%neq-fin-inf-01: ⊦ ⌜x⌝ ≠ σ + ⌜nf0⌝ ;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%stream freely generated by ⌜ ⌝, ⌜ ⌝;;%test-01: ⊦ ¬ finp(⌜nf⌝ ); from specification stream-basic%stream-fin-forward: ⊦ finp(σ) → (∃ x. ⌜x⌝ = σ); (forward) from specification stream-basic%test-02: ⊦ finp(⌜x⌝ ); from specification stream-basic%stream-inf-forward: ⊦ ¬ finp(σ) → (∃ nf. ⌜nf⌝ = σ); (forward) from specification stream-basic%disj: ⊦ ⌜x⌝ ≠ ⌜nf⌝ ; from specification stream-basic