File:Inductive proofs of properties of add, mult from recursive definitions (exercise version).pdf
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DescriptionInductive proofs of properties of add, mult from recursive definitions (exercise version).pdf |
English: English: Shows recursive definitions of addition (+) and multiplication (*) on natural numbers and inductive proofs of commutativity, associativity, distributivity by Peano induction; some of the later ones are omitted as exercises. Also indicates which property is used in the proof of which other one. |
Date | |
Source | Adapted from File:Inductive proofs of properties of add, mult from recursive definitions.pdf |
Author | Adapted by me; the original is by User:Jochen_Burghardt. |
LaTeX source code |
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& 0+0 & \\
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& 0+Sx & \\
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= & Sx & \rs{I.H.} \\
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\\[50mm]
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\begin{tabular}{ll|}
\hline
\multicolumn{2}{l|}{\bf Legend:} \\
$S(x)$ & Successor of $x$ \\
Def. & Definition \\
Lem. & Lemma \\
I.H. & Induction Hypothesis \\
\multicolumn{2}{l|}{\bf Binding Priorities:} \\
%\multicolumn{2}{l}{$S$ , $ \cdot $ , $+$} \\
\multicolumn{2}{l|}{$Sx \cdot y+z$ denotes $((S(x)) \cdot y)+z$} \\
\multicolumn{2}{l|}{\bf Used Induction Scheme:} \\
If & $P(0)$ \\
and & $P(x)$ always implies $P(Sx)$, \\
then & always $P(x)$. \\
&\\
\multicolumn{2}{l|}{Red arrow: use of lemma} \\
\multicolumn{2}{l|}{Definition-uses omitted} \\
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current | 21:44, 6 February 2022 | 2,862 × 3,247 (76 KB) | Felix QW (talk | contribs) | Uploaded a work by Adapted by me; the original is by User:Jochen_Burghardt. from Adapted from File:Inductive proofs of properties of add, mult from recursive definitions.pdf with UploadWizard |
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