DIV_CONV : conv
STRUCTURE
reduceLib
SYNOPSIS
Calculates by inference the result of dividing, with truncation, one numeral by another.
LIBRARY
reduce
DESCRIPTION
If m and n are numerals (e.g. 0, 1, 2, 3,...), then DIV_CONV ``m DIV n`` returns the theorem: 
   |- m DIV n = s
where s is the numeral that denotes the result of dividing the natural number denoted by m by the natural number denoted by n, with truncation.
FAILURE
DIV_CONV tm fails unless tm is of the form ``m DIV n``, where m and n are numerals, or if n denotes zero.
EXAMPLE
> DIV_CONV ``0 DIV 0``;
Exception-
   HOL_ERR
  {message = "attempt to divide by zero", origin_function = "DIV_CONV",
  origin_structure = "Arithconv"} raised

> DIV_CONV ``x DIV 12``;
Exception- ...

> DIV_CONV ``0 DIV 12``;
val it = |- 0 DIV 12 = 0 : thm

> DIV_CONV ``7 DIV 2``;
val it = |- 7 DIV 2 = 3 : thm
HOL  Kananaskis-14