Expression of type ExprTuple

from the theory of proveit.linear_algebra.tensors

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 ExprTuple, gamma, i, y
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.logic import CartExp, Equals, InSet
from proveit.numbers import Interval, Mult, Real, four, three, two

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = Interval(two, four)
sub_expr3 = VecSum(index_or_indices = sub_expr1, summand = ScalarMult(i, y), domain = sub_expr2)
expr = ExprTuple(InSet(sub_expr3, CartExp(Real, three)), Equals(ScalarMult(gamma, sub_expr3), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(Mult(gamma, i), y), domain = sub_expr2)).with_wrapping_at(1))

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(\left(\sum_{i=2}^{4} \left(i \cdot y\right)\right) \in \mathbb{R}^{3}, \begin{array}{c} \begin{array}{l} \left(\gamma \cdot \left(\sum_{i=2}^{4} \left(i \cdot y\right)\right)\right) \\  = \left(\sum_{i=2}^{4} \left(\left(\gamma \cdot i\right) \cdot y\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: 30 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	15, 6
4	Literal
5	ExprTuple	7, 8
6	Operation	operator: 9 operands: 10
7	Operation	operator: 28 operands: 11
8	Operation	operator: 17 operand: 16
9	Literal
10	ExprTuple	13, 14
11	ExprTuple	36, 15
12	ExprTuple	16
13	Literal
14	Literal
15	Operation	operator: 17 operand: 20
16	Lambda	parameter: 37 body: 19
17	Literal
18	ExprTuple	20
19	Conditional	value: 21 condition: 26
20	Lambda	parameter: 37 body: 23
21	Operation	operator: 28 operands: 24
22	ExprTuple	37
23	Conditional	value: 25 condition: 26
24	ExprTuple	27, 34
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operands: 31
27	Operation	operator: 32 operands: 33
28	Literal
29	ExprTuple	37, 34
30	Literal
31	ExprTuple	37, 35
32	Literal
33	ExprTuple	36, 37
34	Variable
35	Operation	operator: 38 operands: 39
36	Variable
37	Variable
38	Literal
39	ExprTuple	40, 41
40	Literal
41	Literal