the full text of the resolution 1559 is as follows:
"The Security Council,defenders of israel's actions point to the third and fourth bullet points to justify the current offensive (i.e. "Calls for the disbanding and disarmament of all Lebanese and non-Lebanese militias" and "Supports the extension of the control of the Government of Lebanon over all Lebanese territory.")
"Recalling all its previous resolutions on Lebanon, in particular resolutions 425 (1978) and 426 (1978) of 19 March 1978, resolution 520 (1982) of 17 September 1982, and resolution 1553 (2004) of 29 July 2004 as well as the statements of its President on the situation in Lebanon, in particular the statement of 18 June 2000 (S/PRST/2000/21),
"Reiterating its strong support for the territorial integrity, sovereignty and political independence of Lebanon within its internationally territorially recognized borders,
"Noting the determination of Lebanon to ensure the withdrawal of all non-Lebanese forces from Lebanon,
"Gravely concerned at the continued presence of armed militias in Lebanon, which prevent the Lebanese government from exercising its full sovereignty over all Lebanese territory,
"Reaffirming the importance of the extension of the control of the Government of Lebanon over all Lebanese territory,
"Mindful of the upcoming Lebanese presidential elections and underlining the importance of free and fair elections according to Lebanese constitutional rules devised without foreign interference or influence,
𔄜. Reaffirms its call for the strict respect of the sovereignty, territorial integrity, unity, and political independence of Lebanon under the sole and exclusive authority of the Government of Lebanon throughout Lebanon;
𔄜. Calls upon all remaining foreign forces to withdraw from Lebanon;
𔄜. Calls for the disbanding and disarmament of all Lebanese and non-Lebanese militias;
𔄜. Supports the extension of the control of the Government of Lebanon over all Lebanese territory;
𔄜. Declares its support for a free and fair electoral process in Lebanon's upcoming presidential election conducted according to Lebanese constitutional rules devised without foreign interference or influence;
𔄜. Calls upon all parties concerned to cooperate fully and urgently with the Security Council for the full implementation of this and all relevant resolutions concerning the restoration of the territorial integrity, full sovereignty, and political independence of Lebanon;
𔄜. Requests that the Secretary-General report to the Security Council within thirty days on the implementation by the parties of this resolution and decides to remain actively seized of this matter.
but if you read the overall resolution, it seems pretty clear that israel's actions directly contravenene both the letter and spirit of 1559. specifically, the first two bullet points ("Reaffirms its call for the strict respect of the sovereignty, territorial integrity, unity, and political independence of Lebanon under the sole and exclusive authority of the Government of Lebanon throughout Lebanon" (emphasis added) and "Calls upon all remaining foreign forces to withdraw from Lebanon"). indeed, israel's actions also contravene the spirit of the resolution as expressed in the introductory "whereas"-type clauses at the beginning (e.g. "Noting the determination of Lebanon to ensure the withdrawal of all non-Lebanese forces from Lebanon")
under any fair reading of 1559, israel is violating the resolution by attacking lebanon. while it is true that hezbollah had not disarmed prior to the israeli incursion (so hezbollah was not in compliance with the resolution either) it seems to me that the israeli attack is just adding to the violations, not subtracting from them.
