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, a, alpha, beta, delta, fi, gamma, i, u, v, w, x, y, z
from proveit.linear_algebra import VecSpaces, VecZero
from proveit.logic import CartExp, Forall, InClass, InSet, NotEquals
from proveit.numbers import Complex, Natural, Real, three

# build up the expression from sub-expressions
sub_expr1 = CartExp(Real, three)
sub_expr2 = VecSpaces(Real)
sub_expr3 = VecZero(sub_expr1)
expr = ExprTuple(InSet(u, sub_expr1), InSet(v, sub_expr1), InSet(w, sub_expr1), InSet(x, sub_expr1), InSet(y, sub_expr1), InSet(z, sub_expr1), NotEquals(x, sub_expr3), NotEquals(z, sub_expr3), InSet(a, Real), InSet(alpha, Complex), InSet(beta, Real), InSet(gamma, Real), InSet(delta, Real), Forall(instance_param_or_params = [i], instance_expr = InSet(fi, sub_expr1), domain = Natural), InClass(fi, sub_expr2), InClass(x, sub_expr2))

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(u \in \mathbb{R}^{3}, v \in \mathbb{R}^{3}, w \in \mathbb{R}^{3}, x \in \mathbb{R}^{3}, y \in \mathbb{R}^{3}, z \in \mathbb{R}^{3}, x \neq \vec{0}\left(\mathbb{R}^{3}\right), z \neq \vec{0}\left(\mathbb{R}^{3}\right), a \in \mathbb{R}, \alpha \in \mathbb{C}, \beta \in \mathbb{R}, \gamma \in \mathbb{R}, \delta \in \mathbb{R}, \forall_{i \in \mathbb{N}}~\left(f\left(i\right) \in \mathbb{R}^{3}\right), f\left(i\right) \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(\mathbb{R}\right), x \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(\mathbb{R}\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, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16
1	Operation	operator: 59 operands: 17
2	Operation	operator: 59 operands: 18
3	Operation	operator: 59 operands: 19
4	Operation	operator: 59 operands: 20
5	Operation	operator: 59 operands: 21
6	Operation	operator: 59 operands: 22
7	Operation	operator: 24 operands: 23
8	Operation	operator: 24 operands: 25
9	Operation	operator: 59 operands: 26
10	Operation	operator: 59 operands: 27
11	Operation	operator: 59 operands: 28
12	Operation	operator: 59 operands: 29
13	Operation	operator: 59 operands: 30
14	Operation	operator: 31 operand: 48
15	Operation	operator: 34 operands: 33
16	Operation	operator: 34 operands: 35
17	ExprTuple	36, 62
18	ExprTuple	37, 62
19	ExprTuple	38, 62
20	ExprTuple	49, 62
21	ExprTuple	39, 62
22	ExprTuple	40, 62
23	ExprTuple	49, 41
24	Literal
25	ExprTuple	40, 41
26	ExprTuple	42, 69
27	ExprTuple	43, 44
28	ExprTuple	45, 69
29	ExprTuple	46, 69
30	ExprTuple	47, 69
31	Literal
32	ExprTuple	48
33	ExprTuple	61, 50
34	Literal
35	ExprTuple	49, 50
36	Variable
37	Variable
38	Variable
39	Variable
40	Variable
41	Operation	operator: 51 operand: 62
42	Variable
43	Variable
44	Literal
45	Variable
46	Variable
47	Variable
48	Lambda	parameter: 68 body: 53
49	Variable
50	Operation	operator: 54 operand: 69
51	Literal
52	ExprTuple	62
53	Conditional	value: 56 condition: 57
54	Literal
55	ExprTuple	69
56	Operation	operator: 59 operands: 58
57	Operation	operator: 59 operands: 60
58	ExprTuple	61, 62
59	Literal
60	ExprTuple	68, 63
61	Operation	operator: 64 operand: 68
62	Operation	operator: 66 operands: 67
63	Literal
64	Variable
65	ExprTuple	68
66	Literal
67	ExprTuple	69, 70
68	Variable
69	Literal
70	Literal