Expression of type Conditional

from the theory of proveit.numbers.absolute_value

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, Equals, InSet
from proveit.numbers import Abs, Complex, subtract

# build up the expression from sub-expressions
expr = Conditional(Equals(Abs(subtract(a, b)), Abs(subtract(b, a))), And(InSet(a, Complex), InSet(b, Complex)))

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 - b\right| = \left|b - a\right| \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{C}\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: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 12 operand: 17
8	Operation	operator: 12 operand: 18
9	Operation	operator: 15 operands: 14
10	Operation	operator: 15 operands: 16
11	ExprTuple	17
12	Literal
13	ExprTuple	18
14	ExprTuple	29, 19
15	Literal
16	ExprTuple	28, 19
17	Operation	operator: 21 operands: 20
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	29, 23
21	Literal
22	ExprTuple	28, 24
23	Operation	operator: 26 operand: 28
24	Operation	operator: 26 operand: 29
25	ExprTuple	28
26	Literal
27	ExprTuple	29
28	Variable
29	Variable