Expression of type Conditional

from the theory of proveit.numbers.multiplication

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, a, b
from proveit.logic import And, InSet
from proveit.numbers import IntegerNonPos, Mult, Natural

# build up the expression from sub-expressions
expr = Conditional(InSet(Mult(a, b), Natural), And(InSet(a, IntegerNonPos), InSet(b, IntegerNonPos)))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{\left(a \cdot b\right) \in \mathbb{N} \textrm{ if } a \in \mathbb{Z}^{\leq 0} ,  b \in \mathbb{Z}^{\leq 0}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 13 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9
6	Operation	operator: 10 operands: 11
7	Literal
8	Operation	operator: 13 operands: 12
9	Operation	operator: 13 operands: 14
10	Literal
11	ExprTuple	15, 16
12	ExprTuple	15, 17
13	Literal
14	ExprTuple	16, 17
15	Variable
16	Variable
17	Literal