`X : β―βΊ πΈ
`X = val β¨ x β© β¨ y β© β¨ z β© y `Β· (x `Β· x `Β· y) `Β· z
`Z : β―βΊ πΈ
`Z = record
{ fst = `X β `X
; snd = subst β_β (sym (abs-Ξ²β [] (`X β· []))) (absβ _ _)
}
abstract
`Zββ : β x β β β `Z β x β
`Zββ {x} xh = subst β_β (sym (abs-Ξ²β [] ((x , xh) β· `X β· []))) (absβ _ _)
`Z-Ξ² : β x β β β y β β `Z β x β y β‘ x β (`Z β x) β y
`Z-Ξ² {x} {y} xh yh =
`X β `X β x β y β‘β¨ abs-Ξ²β [] ((y , yh) β· (x , xh) β· `X β· []) β©
x β (`X β `X β x) β y β‘β¨β©
x β (`Z β x) β y β