Expression of type ExprTuple

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

# build up the expression from sub-expressions
sub_expr1 = subtract(k, two)
sub_expr2 = Conditional(sub_expr1, InSet(k, Interval(nine, nine)))
sub_expr3 = Conditional(sub_expr1, InSet(k, Interval(Add(eight, one), nine)))
expr = ExprTuple(Forall(instance_param_or_params = [k], instance_expr = Equals(sub_expr3, sub_expr2)), Equals(Lambda(k, sub_expr3), Lambda(k, sub_expr2)).with_wrapping_at(2))

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(\forall_{k}~\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), \begin{array}{c} \begin{array}{l} \left[k \mapsto \left\{k - 2 \textrm{ if } k \in \{8 + 1~\ldotp \ldotp~9\}\right..\right] =  \\ \left[k \mapsto \left\{k - 2 \textrm{ if } k \in \{9~\ldotp \ldotp~9\}\right..\right] \end{array} \end{array}\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

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