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Proof step 1 from proof zero-len (conclusion)

⊦ ⌜0⌝ < # σ ↔ σ ≠ []

User applied rule structural induction

And closed the goal!

Rule argument

indvar: σ

Additional information

Used simplifier rules: size-fin: ⊦ # ⌜x⌝ = ⌜# x⌝ ;%fin-empty: ⊦ ⌜x⌝ = [] ↔ x = [];%size-inf: ⊦ # ⌜nf⌝ = ∞;%fun-nonempty: ⊦ [] ≠ ⌜nf⌝ ;%stream freely generated by ⌜ ⌝, ⌜ ⌝;;%zerols-neqzero: ⊦ ⌜0⌝ < n∞ ↔ n∞ ≠ ⌜0⌝ ; from specification nat-inf%disj: ⊦ ⌜m⌝ ≠ ∞; from specification nat-inf-basic%inj: ⊦ ⌜m⌝ = ⌜m0⌝ ↔ m = m0; from specification nat-inf-basic%l: ⊦ # x = 0 ↔ x = []; from specification list-data