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Aug 6 at 16:07 comment added Andreas Blass @AlecRhea The use of function equality to express quantification can be pushed to define quantification as just an abbreviation for certain equations between functions. $\forall x\,\psi(x)$ abbreviates $(\lambda x\,\psi(x))=(\lambda x\,\top)$.
Aug 4 at 20:03 comment added Alec Rhea Thank you Qiaochiu, this clarifies things for me.
Aug 4 at 20:03 vote accept Alec Rhea
Aug 4 at 20:02 history edited Qiaochu Yuan CC BY-SA 4.0
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Aug 4 at 19:56 history answered Qiaochu Yuan CC BY-SA 4.0