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Proof step 7 from proof sub-size-eq (previous step)

# s0 ≤ # s, s ⊆ s0, a ∈ s0 ⊦ a ∈ s

User applied rule insert lemma

And obtained the following new goals

Proof step 8:
⊦ s ⊆ s0 ∧ a ∈ s0 ∧ ¬ a ∈ s → # s < # s0

Rule argument

spec: inst: name: sizesubl seq: ⊦ s ⊆ s0 ∧ a ∈ s0 ∧ ¬ a ∈ s → # s < # s0 subst: [s, s0, a] → [s, s0, a] flags: current, []

Additional information

Used simplifier rules: le-ls-simp: ⊦ m ≤ n → (n < m ↔ false); from specification nat Used terms: s, s0, a