. Ls, Prop := { isAssoc1: ? l1 l2 l3, Lcnd LS l1 l2 -> Lcnd LS (Lprd LS l1 l2) l3 -> Lcnd LS l2 l3; isAssoc2: ? l1 l2 l3, Lcnd LS l1 l2 -> Lcnd LS (Lprd LS l1 l2) l3 -> Lcnd LS l1

, isAssoc3: ? l1 l2 l3, Lcnd LS l2 l3 -> Lcnd LS l1 (Lprd LS l2 l3) -> Lcnd LS l1 l2; isAssoc4: ? l1 l2 l3, Lcnd LS l2 l3 -> Lcnd LS l1 (Lprd LS l2 l3) -> Lcnd LS (Lprd LS l1 l2) l3; isAssoc5: ? l1 l2 l3, Lcnd LS l1 l2 -> Lcnd LS (Lprd LS l1 l2) l3 -> Lprd LS l1 (Lprd LS l2 l3) = Lprd LS (Lprd LS l1 l2) l3

}. Record, Prop := { isComm1: ? l1 l2, Lcnd LS l1 l2 -> Lcnd LS l2 l1; isComm2: ? l1 l2, Lcnd LS l1 l2 -> Lprd LS l1 l2 =

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