Well, you got it on most parts, the fact is that the war was conceived to be limited and hence the aim was to force Usrael to negotiate giving back the Sinai and the Golan heights in Syria.. So they were only two Arab states at war with Usrael; Egypt and Syria, while some Arab states sent contingents, some battalions and very few brigades,, that was mostly symbolic of the Arab's solidarity.. by the way the Arab name for the whole operation was called "Spark"..which means already that it was very far from fire or total war..The Egyptians and the Syrians had to use their Mig-21s mostly for air-defence and interceptions, yet as a frontline fighters they used successfully in some battles, like the Mansora air battle where the Usraelis lost 17 Mirage and F-4s in one day..
The reality of the war was known to most Arab Nations, that Egypt an Syria were going to wage war against an implanted state imposed by Western powers and supported unconditionally by them, So, from the beginning they knew they were going to take on the US's proxy Usrael (that is why I've coined this name, because it is the truth, without the US Usreal is nil in middle East), hence the US weapons from A to Z and the US heavy diplomacy..
Sadat did send all the Russian that were in Egypt back home, because the Arabs, did not want any Russian involvement, and they were fighting for their dignity and land.. but when the US started sending every military gear to Usrael brand new from its own inventory and from the inventory in Europe, along with fighter pilots!!! The Russians decided, on a voluntary base to send some supplies to Egypt and Syria, most of it was paid for by Arabs, like Algeria..A total of $2 billion worth of supply, While Usrael got more than $50 billion worth of American supplies for free, plus mercenaries from all over the world, Jews and non-Jews alike, from the US, Europe, Australia and others..
Sadat knew somehow that this will happen, So after the first very successful week of the war, he, Kissinger and the Russian foreign affairs minister were already open for a ceasefire.. because the main objective of the war was to force Usrael to negotiate, which it has refused many time before the war.. Now Nixon who was not known to like the Jews that much, has turned 180 degrees and ordered the air and sea bridges of supplies to Usrael..even kissinger who was Jewish himself has refused to send supplies because that would just prolong what was already achieved by the Arabs and sealed..But Nixon went ahead for more bloodshed, actually a whole lot of it and with no results for the Usraelis who had to accept the ceasefire after violating 2 a few days before, where they have tried to Encircle the Egyptian 3rd Army, composed of 20 000 man, very well armed and with lines to the Second Army that Sharon and the two other Usraeli generals tries to encircle first, without success, then they have tried to take 2 small cities, Suez and Ismaelia where they have encountered not only the military but also civilians took arms and defeated the Usraelis, after all these failure the Usraeli best Brigades and Units turned South to try to Encircle the Egyptian 3rd Army.. as one can say the Usraeli plans were hectic and desperate to score some victory..it was obvious that they were trapped on the west side of Sinai after the much talked about "gap" that some "Genie" came to tell them about all of a sudden.. Egypt had 80 000 troops in total at war on the East side of the canal, while the Egyptian army had 400 000 professional soldiers and a total of 800 000 armed forces plus reservists.. Usrael had around 50 000 of its best forces, if not the best, all trapped and fighting on the west side of the canal in Sinai, while both the 2nd and 3rd Egyptian armies were holding their own both on the East side of the canal and in some western part of it.. This is the context of the 1973 war in brief till the end, where nothing had changed since the first few days of the war, only more bloodshed for no results for Usrael..the faith of getting back Sinai to Egypt was sealed, and a sacrifice of one brigade to help ease the pressure on the Syrians, or was it the sacrifice to create the trap where 3 Usraeli Armies or brigades (as they call them) composed of 50 000 of their best men were encircled on the Western side of the canal.. Sadat had shown Henry Kissinger two plans to finish them off, or reason them to go back to Usrael alive by accepting a ceasefire...They have accepted and left the Sinai..on Egyptian terms of the ceasefire..
