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Proof step 26 from proof ADD-lemma (previous step)

s ⊆ S, w ∈ s, w ∈ V0, w ∈ S ⊦ S = ∅, # V0 = 0, s = ∅, V0 ∪ (S \ s) = V0 ∪ (S \ (s -- w)), # s = 0, V0 = ∅, # S = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ s1 = s2 ↔ (∀ a. a ∈ s1 ↔ a ∈ s2)
Proof step 25:
s ⊆ S, w ∈ s, w ∈ V0, w ∈ S ⊦ S = ∅, # V0 = 0, s = ∅, ∀ a. a ∈ V0 ∪ (S \ s) ↔ a ∈ V0 ∪ (S \ (s -- w)), # s = 0, V0 = ∅, # S = 0

Rule argument

[x0lemmaarg: spec-name: set-union instance-name: lemma-name: ext antecedent: succedent: s1 = s2 ↔ (∀ a. a ∈ s1 ↔ a ∈ s2) substlist: [s2, s1] → [V0 ∪ (S \ (s -- w)), V0 ∪ (S \ s)] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 3)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (V0 ∪ (S \ (s -- w)), V0 ∪ (S \ s))]]