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Proof step 3 from proof size-eq (previous step)

∀ key. key ∈ ks0 ↔ key ∈ ks1 ⊦ # ks0 = # ks1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
∀ key. key ∈ ks ↔ key ∈ ks0 ⊦ # ks = # ks0 ↔ true
Proof step 5:
∀ key. key ∈ ks0 ↔ key ∈ ks1 ⊦ # ks0 = # ks1, ∀ key. key ∈ ks0 ↔ key ∈ ks1

Rule argument

spec: set-union, inst: node-index name: size-eq-ext seq: ∀ key. key ∈ ks ↔ key ∈ ks0 ⊦ # ks = # ks0 ↔ true subst: [ks0, ks] → [ks1, ks0] flags: <all paths>

Additional information

Used terms: ks1, ks0