theory ArityAnalysisFixProps imports ArityAnalysisFix ArityAnalysisSpec begin context SubstArityAnalysis begin lemma Afix_restr_subst: assumes "x ∉ S" assumes "y ∉ S" assumes "domA Γ ⊆ S" shows "Afix Γ[x::h=y]⋅ae f|` S = Afix Γ⋅(ae f|` S) f|` S" by (rule Afix_restr_subst'[OF Aexp_subst_restr[OF assms(1,2)] assms]) end end