[WIP] feat(UnionFind): add construction witness#1761
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Oppen wants to merge 6 commits intoleanprover-community:mainfrom
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[WIP] feat(UnionFind): add construction witness#1761Oppen wants to merge 6 commits intoleanprover-community:mainfrom
Oppen wants to merge 6 commits intoleanprover-community:mainfrom
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Remove the redundant `parentD_lt` and `rankD_lt` fields from the `UnionFind` structure, keeping only `arr` and `valid : WF arr`. Prove `WF.parentD_lt` and `WF.rankD_lt` by induction on the `WF` predicate, using `rankD_lt_of_isAncestor` as a helper for the compress case. These theorems are exposed as abbreviations on `UnionFind` for backward compatibility. Also moves `setParentBump_rankD_lt`, `setParent_rankD_lt`, and `linkAux_size` before the `UnionFind` structure definition since they operate on raw arrays and are needed by the WF proofs. The `link` function now requires both `xroot` and `yroot` proofs (previously only `yroot`) to satisfy the `WF.link` constructor.
…_lt from WF" This reverts commit 3a4db44.
…D_lt from WF" This reverts commit 4dc71cf.
…and rankD_lt from WF"" This reverts commit 7d4a613.
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At the moment, this is just for discussion in Zulip conversation
The new file
RankBound.leanis meant to be deleted afterwards. It contains theorems I think I'd need to prove the complexity bounds in CSLib, and would be moved there. Specifically, I care about rank_le_log_subtreeSize. The goal of the PR is enabling me to prove that, so I included it here to make sure it fulfills that goal.The main change is that
UnionFindnow requires thearrargument to carry a proof that it was built by applying certain constructors defined as WF.The
linkoperation now works only between roots of disjoint sets, to avoid depleting members of a set, breaking the rank bounds.