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:[0,8],self:6,self_of_nhd:8,self_sub:1,self_trans_symm:[5,7],selfequivsigmaorbit:7,selfmodul:6,semi:[6,7],semicolon:[2,4],semigroup:6,semir:[6,7],send:[7,10],sens:[0,2,3,4,5,6,7,8,9],sensibl:8,sent:[7,8],separ:[0,1,2,4,5],sequenc:[3,6,8,9,12],seri:7,seriou:[4,6,8],serv:[1,3,4,5,10],set:[0,1,2,4,5,6,7,9,10,12],set_integral_const:10,set_opt:6,setco:6,setlik:6,setminu:3,setoid:[6,7],sets_of_superset:8,setub:2,setup:7,sever:[6,8,10],shade:3,shame:6,sharp:0,shift:[0,1,6,8],shorten:[2,7],shorter:[1,3,4,7,8],shot:8,should:[0,1,2,3,4,5,6,7,8,9],shouldn:8,show:[0,1,2,3,4,5,6,7,8,9,10],shown:[1,5,9,10],side:[0,1,2,3,4,5,6,7,8,9],sight:[2,6],sigma:[5,10],sigmafinit:10,sign:8,signatur:6,signific:3,silent:[5,6],silli:6,silva:0,similar:[1,2,3,5,6,7,8],similarli:[2,3,4,5,7],simp:[0,2,3,4,5,6,7,8,9],simp_rw:7,simpa:[4,7,9],simpl:[2,4,5,6,9],simpler:6,simplex:5,simpli:[0,1,2,3,4,5,6,7,8],simplif:[2,3,4],simplifi:[0,2,3,4,5,8,10],sin:[2,9],sinc:[0,1,2,3,4,5,6,7,8],singl:[0,1,2,3,4,5,6,7,9],singleton:4,sinter:3,sinter_eq_biint:3,situat:[1,3,6,7,8],size:5,skeleton:[5,8],sketch:[2,3,4,8],skill:[0,1,2,3,4],slick:2,slight:3,slightli:[1,6,7,8,9],slow:8,small:[0,2,4,5,8],smaller:[3,4,8],smallest:[4,6,8],smart:4,smul:[5,6,7],smul_add:6,smul_distrib:5,snd:[5,8],snippet:[2,4,5,7],so:[0,1,2,3,4,5,6,7,8,9,10],solut:[0,1,4,6],solv:[0,1,2,3,4,5,6,8],some:[0,1,2,3,4,5,6,7,8,9],somehow:7,someth:[0,1,2,4,6,8],sometim:[1,2,3,4,5,6,7,8],somewhat:[1,3,8],somewher:8,soon:[0,2,6,7,8],sophist:8,sorri:[0,1,2,3,4,5,6,7,8,9],sort:[1,3,4],sosi:2,sosx:2,sound:[3,5,6],sourc:[2,8],space:[1,2,3,5,6,7,10,12],speak:[2,5,7,8],special:[3,4,5,6,7,8,10],specif:[0,1,3,4,5,6],specifi:[1,2,3,4,5,8,9,10],spell:8,split:[1,2,3,4],spot:2,sq_ab:5,sq_add_sq_eq_zero:5,sq_nonneg:1,sqr_eq:4,sqrt:[2,3,4,5],squar:[1,2,4,5,6,7],squiggli:2,ss:3,ssubt:3,stabil:7,stage:[2,5,6],stai:5,stand:[1,2,5,7,8,9],standard:[4,5,6,8],standardsimplex:5,standardtwosimplex:5,start:[1,2,3,4,6,7,8,9,10,12],state:[0,1,2,3,4,6,7,8,9],statement:[0,1,2,3,4,5,6,7,8,9,10],stdsimplex:5,steep:0,steinhau:9,step:[0,1,2,3,4,5,6],stick:[1,2,8,9],still:[0,1,2,3,4,5,6,8,10],stipul:9,stop:6,store:5,stori:6,str:5,straightforward:[2,6],strang:[2,4,7],strategi:[1,2,4],strength:1,strengthen:[1,2,4],stretch:[4,5],strict:[1,2],stricter:9,strictli:[1,2,9],strictmono:8,strictorderedr:1,strike:[1,2],strong:[2,4],strong_induction_on:4,stronger:8,strongli:0,stronglymeasurableatfilt:10,struc:5,structur:[2,4,6,7,8,9,10,12],stuck:6,studi:[6,8],style:[0,1],sub:[3,8,10,12],sub_add_cancel:[1,5],sub_eq_add_neg:1,sub_self:[1,2],sub_sub:1,subgoal:2,subgroup:6,subgroupofmulact:7,subject:5,submodul:7,submonoid:[6,7],subobject:6,subproof:1,subr:6,subscript:1,subsequ:[2,4,8],subset:[1,2,3,5,8,9],subset_def:3,subset_iff:4,subspac:[1,6],substant:4,substanti:0,substitut:[0,2],subsum:4,subtl:[5,7,8],subtleti:[6,7],subtract:[1,4,5],subtyp:[5,6,7,8],succ:[3,4,6],succ_add:4,succ_eq_add_on:4,succ_le_succ:4,succ_mul:4,succ_ne_zero:4,succ_po:4,succe:6,success:6,successor:4,suffic:[1,2,3,7,8],suffici:[4,8],suggest:[0,2,4,5,8],suitabl:[0,1,2,5,8],sum:[1,2,4,5,6,7,8],sum_add_distrib:5,sum_eq:5,sum_eq_on:5,sum_id:4,sum_mul:5,sum_range_succ:4,sum_range_zero:4,sum_sqr:4,summat:4,sumofsquar:2,sumofsquares_mul:2,sunion:3,sunion_eq_biunion:3,sup:[1,4,8],sup_assoc:1,sup_comm:1,sup_eq_closur:7,sup_inf_left:1,sup_inf_right:1,sup_inf_self:1,sup_l:1,superfici:8,superscript:8,suppli:5,support:[0,1,2,3,4,5,6,8],suppos:[1,2,3,4,5,8],suppress:1,supremum:[1,4,6,7],sure:[0,1,2,3,5,6,7],surject:[2,3,7,8],surjf:[2,3],surjg:2,surpris:6,surprisingli:[5,6],swap:5,swapxi:5,sweet:3,sylow:7,symbol:[1,2,5,6,7],symm:[3,4,5,6,7,8,9],symmetr:[2,3,7],symmetri:[3,6],synonym:7,syntact:2,syntax:[0,1,2,4,6],synth:6,synthes:[5,6],synthinst:6,system:[3,4,5,6],t2space:8,t3space:8,t:[0,1,2,3,4,5,6,7,8,10],t_3:8,t_:8,t_x:8,t_y:8,t_z:8,tab:[1,3,4],tackl:6,tactic:[0,1,2,3,4,5,6,7,8,9],tag:[2,3,6],take:[1,2,3,4,5,6,7,8,9,10],taken:[1,2],talk:[4,7,8,9],tantamount:[1,3],target:[1,6,7,8,10],task:[0,2,4,5,6,8],taught:7,tauto:4,tautolog:4,teach:0,tear:6,technic:[1,5,6],techniqu:[2,8],technolog:6,tediou:[1,2,6],tell:[0,2,3,4,5,6,7],temporarili:[1,2],tempt:6,tend:[1,8],tendsto:[8,10],tendsto_attop:8,tendsto_congr:8,tendsto_iff:8,tendsto_integral_of_dominated_converg:10,tendsto_nhds_uniqu:8,tendsto_pow_attop_nhds_0_of_lt_1:8,tendsto_right_iff:8,tendsto_subseq:8,term:[0,1,2,3,4,5,7,8],terminolog:5,ters:6,test:4,text:[0,3,5,8],textbook:[0,1,2],th:4,than:[0,1,2,3,4,5,6,7,8,9],thank:6,thei:[0,1,2,3,4,5,6,7,8,9],them:[0,1,2,3,4,5,6,7,8],theme:3,themselv:[0,4,5],theorem:[0,2,4,5,7,8,9,10,12],theoret:[2,3,8],theori:[0,1,2,3,6,7,8,9,12],therefor:[1,4,5,8],thereof:0,thi:[0,1,2,3,4,5,6,7,8,9,10],thing:[0,1,2,3,4,5,6,8],think:[0,1,2,3,4,5,6,8,9],third:[1,2,3,5,8],thorough:0,those:[0,1,2,3,5,6,7,8,9],though:[2,3,4,5],three:[1,2,4,5,7,8],through:[0,1,3,4,5,6,7,8],thu:[1,3,4,5,8],thumb:4,tighter:[1,3],tightli:5,time:[1,4,5,6,8,9,10],timesav:1,tiresom:8,to_addit:6,to_localinvers:9,tofun:[5,6],togeth:[1,2,3,4,5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class=\"section-number\">1. </span>Introduction","<span class=\"section-number\">2. </span>Basics","<span class=\"section-number\">3. </span>Logic","<span class=\"section-number\">4. </span>Sets and Functions","<span class=\"section-number\">5. </span>Elementary Number Theory","<span class=\"section-number\">6. </span>Structures","<span class=\"section-number\">7. </span>Hierarchies","<span class=\"section-number\">8. </span>Groups and Rings","<span class=\"section-number\">9. </span>Topology","<span class=\"section-number\">10. </span>Differential Calculus","<span class=\"section-number\">11. </span>Integration and Measure Theory","Index","Mathematics in Lean"],titleterms:{"function":[3,8],"schr\u00f6der":3,The:[2,3],about:1,action:7,algebra:[1,5,7],appli:1,asymptot:9,ball:8,basic:[1,6],bernstein:3,build:5,calcul:1,calculu:9,close:8,compact:8,comparison:9,complet:8,concret:7,conjunct:2,continu:[8,9],converg:[2,8],countabl:8,defin:5,differenti:9,disjunct:2,elementari:[4,9,10],exampl:1,existenti:2,fact:1,filter:8,fundament:8,gaussian:5,get:0,group:7,hierarchi:6,ideal:7,ident:1,iff:2,implic:2,index:11,induct:4,infinit:4,integ:5,integr:10,introduct:0,irrat:4,lean:12,lemma:1,linear:9,logic:2,mani:4,map:9,mathemat:12,measur:10,metric:8,monoid:7,more:1,morphism:[6,7],negat:2,norm:9,number:4,object:6,open:8,overview:0,polynomi:7,prime:4,prove:1,quantifi:2,quotient:7,recurs:4,ring:7,root:4,rw:1,separ:8,sequenc:2,set:[3,8],space:[8,9],start:0,structur:[1,5],sub:6,subgroup:7,subr:7,theorem:[1,3],theori:[4,10],topolog:8,uniformli:8,unit:7,univers:2,us:1}})