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, x, y
from proveit.linear_algebra import ScalarMult, TensorProd, VecSum
from proveit.logic import CartExp, Equals, Forall, InSet
from proveit.numbers import Interval, Real, four, three, two

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = ScalarMult(gamma, i)
sub_expr3 = CartExp(Real, three)
sub_expr4 = Interval(two, four)
sub_expr5 = ScalarMult(sub_expr2, y)
expr = ExprTuple(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(TensorProd(x, sub_expr5), TensorProd(sub_expr3, sub_expr3)), domain = sub_expr4), Equals(TensorProd(x, VecSum(index_or_indices = sub_expr1, summand = sub_expr5, domain = sub_expr4)), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr2, TensorProd(x, y)), domain = sub_expr4)).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(\forall_{i \in \{2~\ldotp \ldotp~4\}}~\left(\left(x {\otimes} \left(\left(\gamma \cdot i\right) \cdot y\right)\right) \in \left(\mathbb{R}^{3} {\otimes} \mathbb{R}^{3}\right)\right), \begin{array}{c} \begin{array}{l} \left(x {\otimes} \left(\sum_{i=2}^{4} \left(\left(\gamma \cdot i\right) \cdot y\right)\right)\right) \\  = \left(\sum_{i=2}^{4} \left(\left(\gamma \cdot i\right) \cdot \left(x {\otimes} y\right)\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: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameter: 51 body: 10
8	Operation	operator: 38 operands: 11
9	Operation	operator: 17 operand: 15
10	Conditional	value: 13 condition: 31
11	ExprTuple	44, 14
12	ExprTuple	15
13	Operation	operator: 36 operands: 16
14	Operation	operator: 17 operand: 22
15	Lambda	parameter: 51 body: 19
16	ExprTuple	20, 21
17	Literal
18	ExprTuple	22
19	Conditional	value: 23 condition: 31
20	Operation	operator: 38 operands: 24
21	Operation	operator: 38 operands: 25
22	Lambda	parameter: 51 body: 27
23	Operation	operator: 46 operands: 28
24	ExprTuple	44, 30
25	ExprTuple	29, 29
26	ExprTuple	51
27	Conditional	value: 30 condition: 31
28	ExprTuple	42, 32
29	Operation	operator: 33 operands: 34
30	Operation	operator: 46 operands: 35
31	Operation	operator: 36 operands: 37
32	Operation	operator: 38 operands: 39
33	Literal
34	ExprTuple	40, 41
35	ExprTuple	42, 45
36	Literal
37	ExprTuple	51, 43
38	Literal
39	ExprTuple	44, 45
40	Literal
41	Literal
42	Operation	operator: 46 operands: 47
43	Operation	operator: 48 operands: 49
44	Variable
45	Variable
46	Literal
47	ExprTuple	50, 51
48	Literal
49	ExprTuple	52, 53
50	Variable
51	Variable
52	Literal
53	Literal