Expression of type Lambda

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, Lambda, 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 = Lambda([a, b, c, d], 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(a, b, c, d\right) \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	38, 40, 41, 39
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13, 14
9	Operation	operator: 30 operands: 15
10	Operation	operator: 28 operands: 16
11	Operation	operator: 20 operands: 17
12	Operation	operator: 20 operands: 18
13	Operation	operator: 20 operands: 19
14	Operation	operator: 20 operands: 21
15	ExprTuple	22, 23
16	ExprTuple	24, 25
17	ExprTuple	38, 26
18	ExprTuple	40, 26
19	ExprTuple	41, 26
20	Literal
21	ExprTuple	39, 26
22	Operation	operator: 28 operands: 27
23	Operation	operator: 28 operands: 29
24	Operation	operator: 30 operands: 31
25	Operation	operator: 36 operands: 32
26	Literal
27	ExprTuple	38, 40
28	Literal
29	ExprTuple	41, 39
30	Literal
31	ExprTuple	33, 34
32	ExprTuple	40, 39
33	Operation	operator: 36 operands: 35
34	Operation	operator: 36 operands: 37
35	ExprTuple	38, 39
36	Literal
37	ExprTuple	40, 41
38	Variable
39	Variable
40	Variable
41	Variable