Descent: strengthen OO_cancelL_conn_map ("if" dir of CORS 2.31)#2372
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jdchristensen wants to merge 1 commit into
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Descent: strengthen OO_cancelL_conn_map ("if" dir of CORS 2.31)#2372jdchristensen wants to merge 1 commit into
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Pull request overview
This PR strengthens the lemma OO_cancelL_conn_map in Descent.v (the “if” direction of CORS Prop. 2.31) by weakening the hypothesis on the composite map g ∘ f from O'-connected to O-connected, leveraging improved connectedness results (notably the OO_isconnected_hfiber viewpoint).
Changes:
- Strengthen
OO_cancelL_conn_mapby replacing theIsConnMap O' (g o f)hypothesis withIsConnMap O (g o f). - Simplify the proof of
OO_cancelL_conn_mapusing a fiber-equivalence (hfiber_hfiber_compose_map) andOO_isconnected_hfiber. - Update surrounding documentation comments to reflect the strengthened statement and clarify hypotheses.
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I noticed that one direction of CORS 2.31 (formalized as
OO_cancelL_conn_map) can be strengthened using the improved results in #2371 , replacing an O'-connectedness hypothesis with an O-connectedness hypothesis. And the proof is actually slightly simpler now, asOO_cancelL_conn_mapis just the fibrewise version ofOO_isconnected_hfiber. (I guess it could already have been proved this way before.)