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Proof step 3 from proof range-in-ri-keys-in-ri (previous step)

ri-cons(ri, fs), ax.toSet ⊆ range ri ⊦ keys(fs, ax).toSet ⊆ dom ri

User applied rule structural induction

And obtained the following new goals

Proof step 4:
ri-cons(ri, fs), (adr + ax0).toSet ⊆ range ri, ∀ ri, fs. ri-cons(ri, fs) ∧ ax0.toSet ⊆ range ri → keys(fs, ax0).toSet ⊆ dom ri ⊦ keys(fs, adr + ax0).toSet ⊆ dom ri

Rule argument

indvar: ax

Additional information

Used simplifier rules: address-list freely generated by [], +;;% ⊦ [].toSet = ∅; (s)% ⊦ ∅ ⊆ as; (s)% ⊦ keys(fs, []) = []; (s)% ⊦ [].toSet = ∅; (s)% ⊦ ∅ ⊆ ks; (s)