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, InSet
from proveit.numbers import Abs, Add, Complex, LessEq

# build up the expression from sub-expressions
expr = Conditional(LessEq(Abs(Add(a, b)), Add(Abs(a), Abs(b))), 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| \leq \left(\left|a\right| + \left|b\right|\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: 23 operand: 16
8	Operation	operator: 20 operands: 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprTuple	16
12	ExprTuple	17, 18
13	ExprTuple	25, 19
14	Literal
15	ExprTuple	26, 19
16	Operation	operator: 20 operands: 21
17	Operation	operator: 23 operand: 25
18	Operation	operator: 23 operand: 26
19	Literal
20	Literal
21	ExprTuple	25, 26
22	ExprTuple	25
23	Literal
24	ExprTuple	26
25	Variable
26	Variable