[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

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

⊦ a ∈ st \ (dom st \ s) ↔ a ∈ st ∧ a ∈ s

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ a ∈ st \ s ↔ a ∈ st ∧ ¬ a ∈ s

Rule argument

spec: inst: name: Diff-ext seq: ⊦ a ∈ st \ s ↔ a ∈ st ∧ ¬ a ∈ s subst: [s, st, a] → [dom st \ s, st, a] flags: rewrite, current

Additional information

Used simplifier rules: Dom: ⊦ a ∈ dom st ↔ a ∈ st;%Difference: ⊦ a ∈ s1 \ s2 ↔ a ∈ s1 ∧ ¬ a ∈ s2; from specification set-union Used terms: dom st \ s, st, a