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 Function, Lambda, f, n
from proveit.logic import Equals
from proveit.numbers import Add, Interval, Sum, one, zero

# build up the expression from sub-expressions
sub_expr1 = [n]
expr = Lambda(f, Equals(Sum(index_or_indices = sub_expr1, summand = Function(f, sub_expr1), domain = Interval(zero, one)), Add(Function(f, [zero]), Function(f, [one]))))

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())

f \mapsto \left(\left(\sum_{n = 0}^{1} f\left(n\right)\right) = \left(f\left(0\right) + f\left(1\right)\right)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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