. . . . . . . . . . . . . . . 18 8 External dependencies 19 i ii CONTENTS III Manual 21 9 Ge�ng Started 23 9.1 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 11 Integers and Floa�ng-Point Numbers 31 11.1 Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 11.2 Floa�ng-Point Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Floa�ng-point zero . . . . . . . . . . . . . . . . .

. 18 8 External dependencies 19 i ii CONTENTS 9 Deprecated or removed 21 III Manual 23 10 Ge�ng Started 25 10.1 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 12 Integers and Floa�ng-Point Numbers 33 12.1 Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 12.2 Floa�ng-Point Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Floa�ng-point zero . . . . . . . . . . . . . . . . .

Deprecated or removed 19 9 External dependencies 21 10 Tooling Improvements 23 III Manual 25 11 Ge�ng Started 27 11.1 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 13 Integers and Floa�ng-Point Numbers 35 13.1 Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 13.2 Floa�ng-Point Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Floa�ng-point zero . . . . . . . . . . . . . . . . .

. 18 i ii CONTENTS 8 External dependencies 19 9 Tooling Improvements 21 III Manual 23 10 Ge�ng Started 25 10.1 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 12 Integers and Floa�ng-Point Numbers 33 12.1 Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 12.2 Floa�ng-Point Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Floa�ng-point zero . . . . . . . . . . . . . . . . .

. 16 7 External dependencies 17 8 Deprecated or removed 19 i ii CONTENTS III Manual 21 9 Ge�ng Started 23 9.1 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 11 Integers and Floa�ng-Point Numbers 31 11.1 Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 11.2 Floa�ng-Point Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Floa�ng-point zero . . . . . . . . . . . . . . . . .

. 16 7 External dependencies 17 8 Deprecated or removed 19 i ii CONTENTS III Manual 21 9 Ge�ng Started 23 9.1 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 11 Integers and Floa�ng-Point Numbers 31 11.1 Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 11.2 Floa�ng-Point Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Floa�ng-point zero . . . . . . . . . . . . . . . . .

T he D e fini t i v e G ui de t o Y i i 1 . 0 Q i a ng X ue a nd X i a ng W e i Z huo C op y r i gh t 2008- 2009. Al l R i gh t s R e s e r v e d . C o n t e n t s C on t e n t s i L i c e n s e i H E P O S S I B I L I T Y O F S U C H D A M A G E . x C o n t e n t s C h a p t e r 1 G e t t i ng St a r t e d 1 . 1 T he D e fini t i v e G ui de t o Y i i T h i s t u t or i al i s r e l e as e s e r v e r s an d p l at f or m s p r ov i d e d P HP 5 i s s u p p or t e d . 1 . 5 C r e a t i ng F i r s t Y i i A ppl i ca t i o n T o ge t an i n i t i al e x p e r i e n c e w i t h Yi i , w e

T he D e fini t i v e G ui de t o Y i i 1 . 1 Q i a ng X ue a nd X i a ng W e i Z huo C op y r i gh t 2008- 2009. Al l R i gh t s R e s e r v e d . C o n t e n t s C on t e n t s i L i c e n s e x P O S S I B I L I T Y O F S U C H D A M A G E . x i i C o n t e n t s C h a p t e r 1 G e t t i ng St a r t e d 1 . 1 T he D e fini t i v e G ui de t o Y i i T h i s t u t or i al i s r e l e as e am e t e r i z i n g R ou t e s i n UR L R u l e s 1 . 3 U pg r a di ng f r o m V e r s i o n 1 . 0 t o 1 . 1 1 . 3 . 1 C ha ng e s R e l a t e d w i t h M o de l Sce na r i o s • R e m ov e d C M od

?β ⊢⊢⊢ x : ?β App x : ?β ⊢⊢⊢ abs x : ?γ Lam ⊢⊢⊢ (λx , abs x ) : ?α In addition, Lean would generate the following constraints to ensure that all the rule applications are legal: 1. For the application ?γ. Thus, Lean would generate the constraint ?α = ?β → ?γ. 2. For the application of Cst, the type of abs must correspond to the declara- tion as Z → N. Thus, Lean would generate the constraint ?β → cases’, a relative of induction’. It performs a case distinc- tion on its argument but does not generate induction hypotheses. For rgb, the invocation cases’ c transforms a goal ⊢ P[c] into a single subgoal

org)” ] }, { “cell_type”: “markdown”, “metadata”: {}, “source”: [ “You can use backslash \ to generate literal characters which would otherwise have special meaning in the Markdown syntax.n”, “n”, “�\n" "\\*literal asterisks\\*\n", " *literal asterisks*\n", "�n”, “n”, “Use double backslash \ \ to generate the literal $ symbol.” ] }, { “cell_type”: “markdown”, “metadata”: {}, “source”: [ “## Headings” j2GPGXgLsZZgvyOeGTCWeWR+SjXLnlyYkMy505GdORiDErijEpnTkZ05GLDMmeXJitcn5QzPMIumeCz+iv7Z4kwOCQuVtEauN18nG67jdegxKEPEpAUxKgBMSrATErwkxAxExB4ExI40xERPqqiLixxrijwLihiLi14S4tWAuLUALi0gK4tCHjtegx2u47XycdRGphkE