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Proof step 2 from proof restrict-at (previous step)

a ∈ s, a ∈ st ⊦ s = ∅, (st \ (dom st \ s))[a] = st[a], # s = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: Diff-get seq: ⊦ ¬ a ∈ s → (st \ s)[a] = st[a] subst: [a, s, st] → [a, dom st \ s, st] flags: rewrite, current

Additional information

Used simplifier rules: Diff-mems-get: ⊦ a ∈ s → (st \ s)[a] = (∅)[a];%Dom: ⊦ a ∈ dom st ↔ a ∈ st;%Difference: ⊦ a ∈ s1 \ s2 ↔ a ∈ s1 ∧ ¬ a ∈ s2; from specification set-union Used terms: a, dom st \ s, st