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Proof step 7 from proof dups-eqsize (previous step)

# x < # y, ∀ a. a ∈ x ↔ a ∈ y ⊦ # x = # y, y = [], dups(x), dups(y)

User applied rule insert lemma

And obtained the following new goals

Proof step 8:
¬ dups(x), ¬ dups(y), ∀ a. a ∈ x → a ∈ y ⊦ # x ≤ # y
Proof step 9:
# x < # y, ∀ a. a ∈ x ↔ a ∈ y ⊦ ¬ dups(y) ∧ ¬ dups(x) ∧ (∀ a. a ∈ y → a ∈ x), # x = # y, y = [], dups(x), dups(y)

Rule argument

spec: list-dup inst: name: dups-lesize seq: ¬ dups(x), ¬ dups(y), ∀ a. a ∈ x → a ∈ y ⊦ # x ≤ # y subst: [x, y] → [y, x] flags: current, []

Additional information

Used simplifier rules: ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat Used terms: y, x