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 Equals, InSet
from proveit.numbers import Add, Complex, Interval, Mult, Neg, Sum, one

# build up the expression from sub-expressions
expr = Lambda(x, Conditional(Equals(Sum(index_or_indices = [i], summand = x, domain = Interval(a, b)), Mult(Add(b, Neg(a), one), x)), InSet(x, 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())

x \mapsto \left\{\left(\sum_{i = a}^{b} x\right) = \left(\left(b - a + 1\right) \cdot x\right) \textrm{ if } x \in \mathbb{C}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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