text‹ The theory of \emph{general minimal mereology} adds general mereology to minimal mereology.\footnote{ cite‹"casati_parts_1999"› p. 46.} ›
locale GMM = GM + MM begin
text‹ It is natural to assume that just as closed minimal mereology and closed extensional mereology
the same theory, so are general minimal mereology and general extensional mereology.\footnote{For
mistake see cite‹"simons_parts:_1987"› p. 37 and cite‹"casati_parts_1999"› p. 46. The mistake
corrected in cite‹"pontow_note_2004"› and cite‹"hovda_what_2009"›. For discussion of the significance
this issue see, for example, cite‹"varzi_universalism_2009"› and cite‹"cotnoir_does_2016"›.}
this is not the case, since the proof of strong supplementation in closed minimal mereology
the product closure axiom. However, in general minimal mereology, the fusion axiom does not
the product closure axiom. So neither product closure nor strong supplementation are theorems. ›
lemma product_closure: "O x y ==> (∃ z. ∀ v. P v z ⟷ P v x ∧ P v y)"
nitpick [expect = genuine] oops
lemma strong_supplementation: "¬ P x y ==> (∃ z. P z x ∧¬ O z y)"
nitpick [expect = genuine] oops
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