Expression of type Lambda

from the theory of proveit.numbers.summation

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, i, x
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, Complex, Integer, Interval, Mult, Neg, Sum, one

# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(Forall(instance_param_or_params = [x], instance_expr = Equals(Sum(index_or_indices = [i], summand = x, domain = Interval(a, b)), Mult(Add(b, Neg(a), one), x)), domain = Complex), And(InSet(a, Integer), InSet(b, 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\right) \mapsto \left\{\forall_{x \in \mathbb{C}}~\left(\left(\sum_{i = a}^{b} x\right) = \left(\left(b - a + 1\right) \cdot x\right)\right) \textrm{ if } a \in \mathbb{Z} ,  b \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: 45 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operand: 8
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8
6	Literal
7	ExprTuple	9, 10
8	Lambda	parameter: 34 body: 12
9	Operation	operator: 38 operands: 13
10	Operation	operator: 38 operands: 14
11	ExprTuple	34
12	Conditional	value: 15 condition: 16
13	ExprTuple	46, 17
14	ExprTuple	47, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 38 operands: 20
17	Literal
18	Literal
19	ExprTuple	21, 22
20	ExprTuple	34, 23
21	Operation	operator: 24 operand: 28
22	Operation	operator: 26 operands: 27
23	Literal
24	Literal
25	ExprTuple	28
26	Literal
27	ExprTuple	29, 34
28	Lambda	parameter: 42 body: 31
29	Operation	operator: 32 operands: 33
30	ExprTuple	42
31	Conditional	value: 34 condition: 35
32	Literal
33	ExprTuple	47, 36, 37
34	Variable
35	Operation	operator: 38 operands: 39
36	Operation	operator: 40 operand: 46
37	Literal
38	Literal
39	ExprTuple	42, 43
40	Literal
41	ExprTuple	46
42	Variable
43	Operation	operator: 44 operands: 45
44	Literal
45	ExprTuple	46, 47
46	Variable
47	Variable