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to avoid a universe inconsistency with ring #1287

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Aug 8, 2024
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to avoid a universe inconsistency with ring #1287

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4 changes: 2 additions & 2 deletions classical/wochoice.v
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Original file line number Diff line number Diff line change
Expand Up @@ -259,7 +259,7 @@ move=> Rxx Rtr Cch sCS.
pose CSch X := `[< [/\ chain R X, {subset C <= X} & {subset X <= S}] >].
pose Rch (X Y : {pred T}) := `[< {subset X <= Y} >].
have: {in CSch & &, transitive Rch}.
by apply: in3W => X Y Z /asboolP-sXY /asboolP-sYZ; apply/asboolP=> x /sXY/sYZ.
by move=> X Y Z ? ? ? /asboolP-sXY /asboolP-sYZ; apply/asboolP => x /sXY/sYZ.
have /Zorn's_lemma/[apply]: {in CSch, reflexive Rch} by move=> X _; apply/asboolP.
case=> [XX CSchXX XXwo | M /asboolP[Mch sCM sMS] maxM]; last first.
exists M; split=> // X Xch sMX sXS.
Expand Down Expand Up @@ -301,7 +301,7 @@ have initRtr: transitive initR.
move=> R2 R1 R3 /asboolP[D12 R12] /asboolP[D23 R23]; apply/asboolP.
split=> [x /D12/D23// | x y D1x D3y]; rewrite R23 ?(D12 x) //.
by case D2y: (y \in R2.1); [apply: R12 | rewrite (contraFF (D12 y))].
have: {in pwo & &, transitive initR} by apply: in3W.
have: {in pwo & &, transitive initR} by move=> X Y Z ? ? ?; exact: initRtr.
have/Zorn's_lemma/[apply]: {in pwo, reflexive initR} by [].
case=> [C pwoC Cch | [D R] /asboolP/=pwoR maxR].
have /(@wo_chainW ({pred T} * rel T)%type) {}Cch := Cch.
Expand Down
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