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Yirmey,
If you want to play the timeline game, then we can discuss Operation Dawn, a planned Egyptian strike using the exact same troop deployments in the Sinai, called off solely because of the Soviets declaring that they wouldn't intervene on behalf of the Egyptians. The Egyptian response - a redeployment of their forces from the Sinai? Nope. They maintained the same number of troops on the Sinai.
So, the number of troops in the Sinai on May 20 constituted an offensive strike force capability. The person who ordered the implementation of Operation Dawn? One 'Amer, who looks an awful lot like your 'Amer that declared that the deployment was solely for defensive purposes. Oops.
Given the irrationality of Egyptian actions and the lukewarm US support of Israel in the bigger Cold War chess match, the Egyptian de facto declaration of war by closing off an international body of water to Israeli shipping, the eviction of the UNEF that would keep the peace between Israel and Egypt by the Egyptians, and the strong rhetoric beaming from Radio Cairo, jus ad bellum existed for Israel.
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"So little pains do the vulgar take in the investigation of truth, accepting readily the first story that comes to hand." Thucydides 1.20.3
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