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?. Ltlleft, ? (a:Agent )(sl : Strategy) (sr :Strategy), LeadsToLeaf sl ? LeadsToLeaf (? a,l,sl,sr?)

?. Ltlright, ? (a:Agent )(sl : Strategy) (sr :Strategy), LeadsToLeaf sr ? LeadsToLeaf (? a,r,sl,sr?)

. @bullet-?a-s, LeadsT oLeaf s ? ?u : U tility, s2u s a u. ? ?a u v s, LeadsT oLeaf s ? s2u s a u ?

C. Alwleadstoleaf, AlwLeadsToLeaf (?f?) ? ALtL : ? (a:Agent )(c:Choice)(sl sr :Strategy), LeadsToLeaf (?a,c,sl,sr?) ? AlwLeadsToLeaf sl ?AlwLeadsToLeaf sr ? AlwLeadsToLeaf (?a,c,sl,sr?)

S. Coinductive, ?. Strategy, and . Prop, = ? SGPE leaf : ? f :Utility fun, SGPE (?f?) ? SGPE left : ? (a:Agent )(u v : Utility) (sl sr : Strategy), AlwLeadsToLeaf (?a,l,sl,sr?) ? SGPE sl ? SGPE sr ?

?. Sgpe, ? (a:Agent ) (u v :Utility) (sl sr : Strategy), AlwLeadsToLeaf (?a,r,sl,sr?) ? SGPE sl ? SGPE sr ?