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, c, d
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Integer, Mult, frac

# build up the expression from sub-expressions
expr = Conditional(Equals(Add(frac(a, b), frac(c, d)), frac(Add(Mult(a, d), Mult(b, c)), Mult(b, d))), And(InSet(a, Integer), InSet(b, Integer), InSet(c, Integer), InSet(d, Integer)))

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(\frac{a}{b} + \frac{c}{d}\right) = \frac{\left(a \cdot d\right) + \left(b \cdot c\right)}{b \cdot d} \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  c \in \mathbb{Z} ,  d \in \mathbb{Z}\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, 11, 12
7	Operation	operator: 28 operands: 13
8	Operation	operator: 26 operands: 14
9	Operation	operator: 18 operands: 15
10	Operation	operator: 18 operands: 16
11	Operation	operator: 18 operands: 17
12	Operation	operator: 18 operands: 19
13	ExprTuple	20, 21
14	ExprTuple	22, 23
15	ExprTuple	36, 24
16	ExprTuple	38, 24
17	ExprTuple	39, 24
18	Literal
19	ExprTuple	37, 24
20	Operation	operator: 26 operands: 25
21	Operation	operator: 26 operands: 27
22	Operation	operator: 28 operands: 29
23	Operation	operator: 34 operands: 30
24	Literal
25	ExprTuple	36, 38
26	Literal
27	ExprTuple	39, 37
28	Literal
29	ExprTuple	31, 32
30	ExprTuple	38, 37
31	Operation	operator: 34 operands: 33
32	Operation	operator: 34 operands: 35
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	38, 39
36	Variable
37	Variable
38	Variable
39	Variable