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Commit 2020-07-06 16:58 f06e4e00

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feat(data/sym2) Defining the symmetric square (unordered pairs) (#3264) This adds a type for the symmetric square of a type, which is the quotient of the cartesian square by permutations. These are also known as unordered pairs. Additionally, this provides some definitions and lemmas for equalities, functoriality, membership, and a relationship between symmetric relations and terms of the symmetric square. I preferred sym2 over unordered_pairs out of a combination of familiarity and brevity, but I could go either way for naming.

Estimated changes

added theorem sym2.congr_right
added def sym2.diag
added theorem sym2.eq_iff
added theorem sym2.eq_swap
added def sym2.equiv_sym
added def sym2.from_rel
added theorem sym2.from_rel_prop
added def sym2.is_diag
added def sym2.map
added theorem sym2.map_comp
added theorem sym2.map_id
added def sym2.mem
added theorem sym2.mem_iff
added theorem sym2.mem_other_spec
added theorem sym2.mk_has_mem
added def sym2.mk_has_vmem
added theorem sym2.rel.symm
added theorem sym2.rel.trans
added inductive sym2.rel
added def sym2.vmem.other
added def sym2.vmem
added theorem sym2.vmem_other_spec
added def sym2