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Based on a dyadic approximation of It\^o integrals, we show the existence ofIt\^o c\`adl\`ag rough paths above general semimartingales, suitable Gaussianprocesses and non-negative typical price paths. Furthermore, Lyons-Victoirextension theorem for c\`adl\`ag paths is presented, stating that everyc\`adl\`ag path of finite $p$-variation can be lifted to a rough path.

Examples of It\^o c\`adl\`ag rough paths