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feat: Rounding Proof: Galois Connection [3/?]#49

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bollu wants to merge 45 commits intomainfrom
proof-round-3-of-x
Open

feat: Rounding Proof: Galois Connection [3/?]#49
bollu wants to merge 45 commits intomainfrom
proof-round-3-of-x

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@bollu bollu commented Feb 9, 2026

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bollu added 15 commits February 18, 2026 14:47
the next thing we need to know is that the packed float ordering is
discrete with endpoints, which means that we need a separation like
theorem that says that there exists a 'successor' and 'predecessor' packed float from every
packed float, and that 'lower = upper \/ successor lower = upper'.

I will probably first prove 'successor' exists, and then defining
the rest of the theory based on this.
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