Expression of type Conditional

from the theory of proveit.numbers.addition

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 Add, Natural, one

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

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 + \left(b + 1\right)\right) = \left(\left(a + b\right) + 1\right) \textrm{ if } a \in \mathbb{N} ,  b \in \mathbb{N}\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: 20 operands: 11
8	Operation	operator: 20 operands: 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprTuple	23, 16
12	ExprTuple	17, 22
13	ExprTuple	23, 18
14	Literal
15	ExprTuple	24, 18
16	Operation	operator: 20 operands: 19
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	24, 22
20	Literal
21	ExprTuple	23, 24
22	Literal
23	Variable
24	Variable