CADiZ

Reference manual / section prelude


section prelude

generic (\power _)

generic 8 rightassoc (_ \cross _)

[\arithmos]


\nat : \power \arithmos
\where
0 \in \nat
1 \in \nat

function 30 leftassoc (_ + _)


_ + _ : \power ((\arithmos \cross \arithmos) \cross \arithmos)
\where
\forall m, n: \nat @ \exists1 p: ( _ + _ ) @ p.1 = (m, n)
\forall m, n: \nat @ m + n \in \nat
\forall m, n: \nat | m + 1 = n + 1 @ m = n
\forall n: \nat @ \lnot n + 1 = 0
\forall w: \power \nat | 0 \in w \land (\forall y: w @ y + 1 \in w) @ w = \nat
\forall m: \nat @ m + 0 = m
\forall m, n: \nat @ m + (n + 1) = (m + n) + 1

IT 3-Jan-2002