equal
deleted
inserted
replaced
1 % |
1 % |
2 \begin{isabellebody}% |
2 \begin{isabellebody}% |
3 \def\isabellecontext{Induction}% |
3 \def\isabellecontext{Induction}% |
|
4 \isamarkupfalse% |
4 % |
5 % |
5 \isadelimtheory |
6 \isadelimtheory |
6 % |
7 % |
7 \endisadelimtheory |
8 \endisadelimtheory |
8 % |
9 % |
9 \isatagtheory |
10 \isatagtheory |
10 \isamarkupfalse% |
|
11 % |
11 % |
12 \endisatagtheory |
12 \endisatagtheory |
13 {\isafoldtheory}% |
13 {\isafoldtheory}% |
14 % |
14 % |
15 \isadelimtheory |
15 \isadelimtheory |
118 The same game can be played with other datatypes, for example lists, |
118 The same game can be played with other datatypes, for example lists, |
119 where \isa{tl} is the tail of a list, and \isa{length} returns a |
119 where \isa{tl} is the tail of a list, and \isa{length} returns a |
120 natural number (remember: $0-1=0$):% |
120 natural number (remember: $0-1=0$):% |
121 \end{isamarkuptext}% |
121 \end{isamarkuptext}% |
122 \isamarkuptrue% |
122 \isamarkuptrue% |
123 \isamarkupfalse% |
|
124 \isacommand{lemma}\isamarkupfalse% |
123 \isacommand{lemma}\isamarkupfalse% |
125 \ {\isachardoublequoteopen}length{\isacharparenleft}tl\ xs{\isacharparenright}\ {\isacharequal}\ length\ xs\ {\isacharminus}\ {\isadigit{1}}{\isachardoublequoteclose}\isanewline |
124 \ {\isachardoublequoteopen}length{\isacharparenleft}tl\ xs{\isacharparenright}\ {\isacharequal}\ length\ xs\ {\isacharminus}\ {\isadigit{1}}{\isachardoublequoteclose}\isanewline |
126 % |
125 % |
127 \isadelimproof |
126 \isadelimproof |
128 % |
127 % |
651 equation. |
650 equation. |
652 |
651 |
653 The proof is so simple that it can be condensed to% |
652 The proof is so simple that it can be condensed to% |
654 \end{isamarkuptext}% |
653 \end{isamarkuptext}% |
655 \isamarkuptrue% |
654 \isamarkuptrue% |
656 \isamarkupfalse% |
|
657 % |
655 % |
658 \isadelimproof |
656 \isadelimproof |
659 % |
657 % |
660 \endisadelimproof |
658 \endisadelimproof |
661 % |
659 % |
673 \isadelimtheory |
671 \isadelimtheory |
674 % |
672 % |
675 \endisadelimtheory |
673 \endisadelimtheory |
676 % |
674 % |
677 \isatagtheory |
675 \isatagtheory |
678 \isamarkupfalse% |
|
679 % |
676 % |
680 \endisatagtheory |
677 \endisatagtheory |
681 {\isafoldtheory}% |
678 {\isafoldtheory}% |
682 % |
679 % |
683 \isadelimtheory |
680 \isadelimtheory |