From 0ffbdaf39cab1b705ef07e634bd2e4d8052cb985 Mon Sep 17 00:00:00 2001 From: Jlh18 Date: Sun, 7 Nov 2021 12:54:58 +0000 Subject: [PATCH] extend solutions for fund / Q3 using trin / Q5 --- 1FundamentalGroup/Quest3Solutions.agda | 22 +++++++----------- .../1FundamentalGroup/Quest3Solutions.agdai | Bin 35642 -> 39214 bytes 2 files changed, 8 insertions(+), 14 deletions(-) diff --git a/1FundamentalGroup/Quest3Solutions.agda b/1FundamentalGroup/Quest3Solutions.agda index 849ce06..8f4be97 100644 --- a/1FundamentalGroup/Quest3Solutions.agda +++ b/1FundamentalGroup/Quest3Solutions.agda @@ -1,21 +1,15 @@ module 1FundamentalGroup.Quest3Solutions where -open import Cubical.Foundations.Prelude open import Cubical.HITs.S1 using ( S¹ ; base ; loop ) open import 1FundamentalGroup.Quest1Solutions +open import Cubical.Foundations.Prelude renaming (transport to pathToFun) open import Cubical.Foundations.Path - -outOfS¹ : (B : S¹ → Type) → (b : B base) → PathP (λ i → B (loop i)) b b → (x : S¹) → B x -outOfS¹ B b p base = b -outOfS¹ B b p (loop i) = p i - - +open import 0Trinitarianism.Quest5Solutions rewind : (x : S¹) → helix x → base ≡ x -rewind base = loop_times -rewind (loop i) = path i where - - path : PathP (λ i → helix (loop i) → base ≡ loop i) loop_times loop_times - path = {!!} - -thing = PathPIsoPath +rewind = outOfS¹D (λ x → helix x → base ≡ x) loop_times + ( + pathToFun (λ i → sucℤPath i → base ≡ loop i) loop_times + ≡⟨ {!!} ⟩ + loop_times ∎ + ) diff --git a/_build/2.6.2/agda/1FundamentalGroup/Quest3Solutions.agdai b/_build/2.6.2/agda/1FundamentalGroup/Quest3Solutions.agdai index 7f2ff9fd8b804ca126766059315ec52622ef3df1..bcd1697b8e8dd40b3fb85a96e293e17b7a30dd37 100644 GIT binary patch literal 39214 zcmYIw2UrtX_x_!kGN4a9 z-8d#Xm?nnt<%Uv}3YWK;iJ7@@c{S3kFo4UZ!)eMWI)Wyw0Ne6M1lt|SDlDpBr!(Yy zYQm9Nw~NTAGn!uMk<2yf%w+Cv`9O&3SK?0%QN2Esd!VMmO^Wo$8QVVO5KIo4Pk3DPIf!Oix=4MtM5mYm?}aK%W>T*cQ#?gJqYI3OhEyTzpDW?d}!`ASVO zvxo46>wL~5w!5B8=8|U#e^|>N!5_|SQ9YYEaA58SW`xq*Y=dv{ik>J%ruddmXg;C& zQAE#fwofLFI$hKk?uJpOsYh|V$TI5u1iH@speL%Is6JZ&XN!0k>nO(hm-;Lzsy{?v zP1vBxG6J8ShR>?ib4U0~4g4kH&KEOSsq=|^DRPB-*I8(b>N%kB4BaMB_#pw>bwyi% zz^x$giMv1#Abf?9*IDHM0%EARo?}g?8S*wC^!&L2v3IygPsdK!1G-t_KZ23w$LXNY z3=>N8qbC0200{U|Eg%n|U*h5cLcDom<{9Y;IP4FA;z{G@&k*bz1eon-yDQ)%b3z9I z01G{^n8jcy2emx5QRg3Oxh{zV2s6G+u)pDPfz5}Ph7xXT+sYNqNf$yx(ECY ze}cC^>ccJTFA_$bu>kgek=dY(FIYPA=b6~j7||Jgb14kw6$6}jh$eU@H<~fzE?t={ z(cvkGV1u2HNA8C^Yr%u=h8q%1q$mnpeKPMF77_v4yx%+vz5^vLHXMX|De(ore;#kp z^M0%Fpf}q~sZhFMAvd_%{N!}24HX1ytee4vB2lbTwHhjRb1nHB5WSI>*32~BZZ zmNm-yAJb{d96+5%8QsYJxyH=hf=`p_j~nQfcIlMh&D$GV+h1Q7tkf3KT%*1_dg#ss z`eP~`j6QPd*AW<%9iYk}wLf`n{B7|!GrN33$FJe#KU&gDDa}V$jJ{s*Wg41LyQl6= z0;9Xb#PbO0*%`DASoh6x46(kDn&zLv=u=g1N;|&&Q9br8g8t}4uQVihN2mZznLc`q zEI%&X_CZJV?UXjMnGK+RVhIW*p`JhG>o+lXO-TL+g7*^%n*V7cUd3dffGWypR$(tO zd%FLT!gH&*`OX}pKXX6u%Ci6Vz4b>@v9fUu-H^7*@xQK8YSVB0d4#2N6Mux*H^r`+ z3^+n*nzwFZZf$uJ=;Ybg-g=Y>Sd27JwDd8$|4hq`n_!G~a7Z28w#|Me0^ zYV$mJpy3v0X^X1$5+mV)Em}`AHpd8%J07%@Mumd zh>129u9^z^bx)xW{;xZZZuyhB8#KVLmzw~_eh%Wp*y9qIR8 z?m-hgj(F#v)avcLxl((=A;@&d=Q% zjLps&H;*lwKkW{f_+aqCd4xak9tBRbJ4$J`{Keco)xCwb3$qP#2qUyni!oxzfgk9P ze3}~AhCt{tjX1^yDX6#Bso$*q(tkfn*gPbSW*s!6KPJ-Lllu;w!vS(&HDmkG;UTem znU3hcnck+(_7N*xXB~RGa<_}LBIiEx?6lYh^=zl^O%8v{RA~!mAfR4y8*P6*ZNL^= zyU)gz(RDYqOeOa%n|+DeecMR9irQ%w9kL?p*S7Ch8~|36+C<=rxoglJBVqUdATlNI z3CjvA%R`LqvxCpbfKh8K)f1%dyPXS%6*%aWck%6Gx3gX#k#rWZ??njQ>_}KfCQZL- zMQn@y-@5LUZS+C6LN_8{)Ka|az-=>e_i-dBbd#)wVy7eGbRX}IKPLQ)csos{Ev_vYMAlYhGo}Mkw^L8b+%ge&*R0~mG8?KS zSM_PG?uem>xfi+bcJVI6AMmFSdJOo1bF6RXy_n;>8x*v?+TFkqCN06v{(lqvfpGfZ ziI!$`XEtF|j2*GdKup(65On$-JfxGnm(@<38FK^ zy260J#Sv!-LPj{yEoAXqYkB_*#naYX2RixY4&yES0CXjmT2R| zr37HKCUXAh4r4go57kB@47;5W@9Sh~%d?gabmt}`siQnedKCJu82VsFp&89pY?;!` zmu03*KN9OAZK)G6V#4V78BJ&VF9%awYkp|JG4|8{QJhFACvyJZE}Y#H$bB#7O(j`x ziGX+tm@$(ONZuYYJrp4^FVhv(v!rF`Fh^3Xl4n!fq?dl%6v+~;PhHQY%Pfh&zspXc z+3UU5Yh2sij!Q^j{JdTg+_{9a$_kxMW*c4Gy+oHcs>4^LgEz&K5nJBMlne_YmMm`T zd1w>cIy={G5mdp2rq|qra$m-FtK2?1q<3y_Xm98O9Gopvt{FJjlh?)x(#sXC->w*C zI(N}!D#DVG>LMd?1hMZw4p?OJ6b}kSR$S}W{=gF{q7{6)j7#pjAHIjomHW#x;lTMB zNN1@FC_PC-3=`U)B;k;duCU@O;-Es7#RAMlDA01=8f57{c&&Q|5P5b-P-w#ersP0r zDBA6*55efE;e7VMnZ@B3$_`<+tvce#2AoNg)I>hT5v@1AHi5qk@rI(Y%$W?i-bY&I z+Nv$3_UtOQ*pECnx9qjpe~u}6Q1X-rIHd!z;lpx1`*h)2@mlfQXtnA?;(DYdZ&1gZ zVi_F{Cy1;)RKO`c@YFRch&Q%a-hgEWzX+HX0C3-&=(hc!EmG*q0~v7v3w&?I7A!Pf zXeu@p7c{B8uW*4NE^Cg-x=#t^zcD4#q*h$sG}i7E68J5j$dKPAh~fku{X ze>vPHo}+!YPNooO3YqQ&7A#*_~AHB6<;w> z(`Yr&nM}!=vJJ!?P|JygY?I<5MX_}FGb}QBMc#WzV97;ILog?j-zz&x1=Nt>qm+r! 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