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Proof step 5 from proof H-dom-subset (previous step)

dom H ⊆ dom map, r ∈ H ⊦ r ∈ map

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ rs ⊆ rs0 ↔ (∀ r. r ∈ rs → r ∈ rs0)

Rule argument

spec:set-basic inst:refset name:Subset seq: ⊦ rs ⊆ rs0 ↔ (∀ r. r ∈ rs → r ∈ rs0) subst:[rs0, rs] → [dom map, dom H] flags:rewrite

Additional information

[Concretesimprules(()), Extraterms((dom mapdom H))]