previous up next
Go backward to Inductive Function Definitions
Go up to Top
Go forward to Induction with Larger Decrements
RISC-Linz logo

Inductively Defined Function

Let A0, ..., Ai-1, Ai+1, ..., An-1, B such that we have

Tb in B /\  Tr in B
for all x0 in A0, ..., xi-1 in Ai-1, xi in N, xi+1 in Ai+1, ..., xn-1 in An-1. Then the definition introduces the unique function
f: A0 x ... x Ai-1 x N x Ai+1 x ... x An-1 -> B
that satisfies
f(x0, ..., 0, ..., xn-1) = Tb /\ 
f(x0, ..., xi+1, ..., xn-1) = Tr
for all x0 in A0, ..., xi-1 in Ai-1, xi in N, xi+1 in Ai+1, ..., xn-1 in An-1.
Author: Wolfgang Schreiner
Last Modification: November 24, 1999

previous up next