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, fi, gamma, i, x, y, z
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 = CartExp(Real, three)
sub_expr3 = Interval(two, four)
sub_expr4 = TensorProd(y, fi)
sub_expr5 = ScalarMult(gamma, sub_expr4)
expr = ExprTuple(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(TensorProd(x, sub_expr5, z), TensorProd(sub_expr2, sub_expr2, sub_expr2, sub_expr2)), domain = sub_expr3), Equals(TensorProd(x, VecSum(index_or_indices = sub_expr1, summand = sub_expr5, domain = sub_expr3), z), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(gamma, TensorProd(x, sub_expr4, z)), domain = sub_expr3)).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(\gamma \cdot \left(y {\otimes} f\left(i\right)\right)\right) {\otimes} z\right) \in \left(\mathbb{R}^{3} {\otimes} \mathbb{R}^{3} {\otimes} \mathbb{R}^{3} {\otimes} \mathbb{R}^{3}\right)\right), \begin{array}{c} \begin{array}{l} \left(x {\otimes} \left(\sum_{i=2}^{4} \left(\gamma \cdot \left(y {\otimes} f\left(i\right)\right)\right)\right) {\otimes} z\right) \\  = \left(\sum_{i=2}^{4} \left(\gamma \cdot \left(x {\otimes} \left(y {\otimes} f\left(i\right)\right) {\otimes} z\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: 56 body: 10
8	Operation	operator: 48 operands: 11
9	Operation	operator: 17 operand: 15
10	Conditional	value: 13 condition: 30
11	ExprTuple	43, 14, 45
12	ExprTuple	15
13	Operation	operator: 36 operands: 16
14	Operation	operator: 17 operand: 22
15	Lambda	parameter: 56 body: 19
16	ExprTuple	20, 21
17	Literal
18	ExprTuple	22
19	Conditional	value: 23 condition: 30
20	Operation	operator: 48 operands: 24
21	Operation	operator: 48 operands: 25
22	Lambda	parameter: 56 body: 26
23	Operation	operator: 34 operands: 27
24	ExprTuple	43, 29, 45
25	ExprTuple	28, 28, 28, 28
26	Conditional	value: 29 condition: 30
27	ExprTuple	41, 31
28	Operation	operator: 32 operands: 33
29	Operation	operator: 34 operands: 35
30	Operation	operator: 36 operands: 37
31	Operation	operator: 48 operands: 38
32	Literal
33	ExprTuple	39, 40
34	Literal
35	ExprTuple	41, 44
36	Literal
37	ExprTuple	56, 42
38	ExprTuple	43, 44, 45
39	Literal
40	Literal
41	Variable
42	Operation	operator: 46 operands: 47
43	Variable
44	Operation	operator: 48 operands: 49
45	Variable
46	Literal
47	ExprTuple	50, 51
48	Literal
49	ExprTuple	52, 53
50	Literal
51	Literal
52	Variable
53	Operation	operator: 54 operand: 56
54	Variable
55	ExprTuple	56
56	Variable