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Proof step 5 from proof range-in-ri-keys-in-ri (previous step)

ri-cons(ri, fs), adr ∈ ri, ax0.toSet ⊆ range ri, ∀ ri, fs. ri-cons(ri, fs) ∧ ax0.toSet ⊆ range ri → keys(fs, ax0).toSet ⊆ dom ri ⊦ keys(fs, ax0).toSet ++ fs[adr].key ⊆ dom ri

User applied rule all left

And obtained the following new goals

Proof step 6:
ri-cons(ri, fs), adr ∈ ri, ax0.toSet ⊆ range ri, ri-cons(ri, fs) ∧ ax0.toSet ⊆ range ri → keys(fs, ax0).toSet ⊆ dom ri ⊦ keys(fs, ax0).toSet ++ fs[adr].key ⊆ dom ri

Rule argument

pos: left 4 terms: ri, fs abort: F discard: T computed: T

Additional information

Used terms: ri, fs