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, i, x, y
from proveit.linear_algebra import ScalarMult, TensorProd, VecSum
from proveit.logic import CartExp, Forall, InSet
from proveit.numbers import Add, Interval, Mult, Real, four, one, 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(sub_expr2, sub_expr2)
sub_expr5 = ScalarMult(Mult(i, Add(i, one)), TensorProd(x, y))
expr = ExprTuple(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(sub_expr5, sub_expr4), domain = sub_expr3), InSet(VecSum(index_or_indices = sub_expr1, summand = sub_expr5, domain = sub_expr3), sub_expr4))

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(\left(i \cdot \left(i + 1\right)\right) \cdot \left(x {\otimes} y\right)\right) \in \left(\mathbb{R}^{3} {\otimes} \mathbb{R}^{3}\right)\right), \left(\sum_{i=2}^{4} \left(\left(i \cdot \left(i + 1\right)\right) \cdot \left(x {\otimes} y\right)\right)\right) \in \left(\mathbb{R}^{3} {\otimes} \mathbb{R}^{3}\right)\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: 22 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 16
6	Lambda	parameter: 45 body: 8
7	Operation	operator: 9 operand: 12
8	Conditional	value: 11 condition: 18
9	Literal
10	ExprTuple	12
11	Operation	operator: 22 operands: 13
12	Lambda	parameter: 45 body: 15
13	ExprTuple	17, 16
14	ExprTuple	45
15	Conditional	value: 17 condition: 18
16	Operation	operator: 32 operands: 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	ExprTuple	24, 24
20	Literal
21	ExprTuple	25, 26
22	Literal
23	ExprTuple	45, 27
24	Operation	operator: 28 operands: 29
25	Operation	operator: 30 operands: 31
26	Operation	operator: 32 operands: 33
27	Operation	operator: 34 operands: 35
28	Literal
29	ExprTuple	36, 37
30	Literal
31	ExprTuple	45, 38
32	Literal
33	ExprTuple	39, 40
34	Literal
35	ExprTuple	41, 42
36	Literal
37	Literal
38	Operation	operator: 43 operands: 44
39	Variable
40	Variable
41	Literal
42	Literal
43	Literal
44	ExprTuple	45, 46
45	Variable
46	Literal