MOD_CONV : conv
STRUCTURE
reduceLib
SYNOPSIS
Calculates by inference the remainder after dividing one numeral by another.
LIBRARY
reduce
DESCRIPTION
If m and n are numerals (e.g. 0, 1, 2, 3,...), then MOD_CONV "m MOD n" returns the theorem: 
   |- m MOD n = s
where s is the numeral that denotes the remainder after dividing, with truncation, the natural number denoted by m by the natural number denoted by n.
FAILURE
MOD_CONV tm fails unless tm is of the form "m MOD n", where m and n are numerals, or if n denotes zero.
EXAMPLE
#MOD_CONV "0 MOD 0";;
evaluation failed     MOD_CONV

#MOD_CONV "0 MOD 12";;
|- 0 MOD 12 = 0

#MOD_CONV "2 MOD 0";;
evaluation failed     MOD_CONV

#MOD_CONV "144 MOD 12";;
|- 144 MOD 12 = 0

#MOD_CONV "7 MOD 2";;
|- 7 MOD 2 = 1
HOL  Kananaskis-14