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Proof step 1 from proof fin-size-from2 (conclusion)

⊦ ¬ # σ < ⌜n⌝ ∧ finp(σ) → #(σ from n) = ⌜(# σ).n - n⌝

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: from-fin: ⊦ ⌜x⌝ from n = ⌜x from n⌝ ;%size-fin: ⊦ # ⌜x⌝ = ⌜# x⌝ ;%length-from: ¬ # x < n ⊦ #(x from n) = # x - n;%inj: ⊦ ⌜m⌝ = ⌜m0⌝ ↔ m = m0; from specification nat-inf-basic%sel: ⊦ ⌜m⌝ .n = m; from specification nat-inf-basic%ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf%test-02: ⊦ finp(⌜x⌝ ); from specification stream-basic%stream-fin-forward: ⊦ finp(σ) → (∃ x. ⌜x⌝ = σ); (forward) from specification stream-basic