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, k
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Interval, eight, nine, one, subtract, two

# build up the expression from sub-expressions
sub_expr1 = subtract(k, two)
expr = Lambda(k, Equals(Conditional(sub_expr1, InSet(k, Interval(Add(eight, one), nine))), Conditional(sub_expr1, InSet(k, Interval(nine, nine)))))

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())

k \mapsto \left(\left\{k - 2 \textrm{ if } k \in \{8 + 1~\ldotp \ldotp~9\}\right.. = \left\{k - 2 \textrm{ if } k \in \{9~\ldotp \ldotp~9\}\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: 16 body: 2
1	ExprTuple	16
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Conditional	value: 8 condition: 7
6	Conditional	value: 8 condition: 9
7	Operation	operator: 12 operands: 10
8	Operation	operator: 26 operands: 11
9	Operation	operator: 12 operands: 13
10	ExprTuple	16, 14
11	ExprTuple	16, 15
12	Literal
13	ExprTuple	16, 17
14	Operation	operator: 21 operands: 18
15	Operation	operator: 19 operand: 24
16	Variable
17	Operation	operator: 21 operands: 22
18	ExprTuple	23, 25
19	Literal
20	ExprTuple	24
21	Literal
22	ExprTuple	25, 25
23	Operation	operator: 26 operands: 27
24	Literal
25	Literal
26	Literal
27	ExprTuple	28, 29
28	Literal
29	Literal