mathlib
                                
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                        `partial_order.lift` vs `function.injective.partial_order`
Should we rename
partial_order.lifttofunction.injective.partial_order? Or conversely, should the definitions in this PR be calledlattice.liftetc? It might be worth polling on Zulip.
Originally posted by @eric-wieser in https://github.com/leanprover-community/mathlib/issues/10615#issuecomment-986035004
As of #10615, we currently have:
- preorder.lift,- partial_order.lift,- linear_order.lift
- function.injective.semilattice_sup,- function.injective.lattice_sup,- function.injective.lattice(and all the algebra defs named in this way)
We should try to unify these naming conventions. This is made somewhat tricky by the fact that preorder.lift doesn't take a function.injective argument.