Expression of type ExprTuple

from the theory of proveit.linear_algebra.addition

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 VecZero
from proveit.logic import CartExp, Forall, InSet, NotEquals
from proveit.numbers import Complex, Natural, Real, three

# build up the expression from sub-expressions
sub_expr1 = CartExp(Real, three)
sub_expr2 = 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_expr2), NotEquals(z, sub_expr2), 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))

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)\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
1	Operation	operator: 51 operands: 15
2	Operation	operator: 51 operands: 16
3	Operation	operator: 51 operands: 17
4	Operation	operator: 51 operands: 18
5	Operation	operator: 51 operands: 19
6	Operation	operator: 51 operands: 20
7	Operation	operator: 22 operands: 21
8	Operation	operator: 22 operands: 23
9	Operation	operator: 51 operands: 24
10	Operation	operator: 51 operands: 25
11	Operation	operator: 51 operands: 26
12	Operation	operator: 51 operands: 27
13	Operation	operator: 51 operands: 28
14	Operation	operator: 29 operand: 44
15	ExprTuple	31, 54
16	ExprTuple	32, 54
17	ExprTuple	33, 54
18	ExprTuple	35, 54
19	ExprTuple	34, 54
20	ExprTuple	36, 54
21	ExprTuple	35, 37
22	Literal
23	ExprTuple	36, 37
24	ExprTuple	38, 61
25	ExprTuple	39, 40
26	ExprTuple	41, 61
27	ExprTuple	42, 61
28	ExprTuple	43, 61
29	Literal
30	ExprTuple	44
31	Variable
32	Variable
33	Variable
34	Variable
35	Variable
36	Variable
37	Operation	operator: 45 operand: 54
38	Variable
39	Variable
40	Literal
41	Variable
42	Variable
43	Variable
44	Lambda	parameter: 60 body: 47
45	Literal
46	ExprTuple	54
47	Conditional	value: 48 condition: 49
48	Operation	operator: 51 operands: 50
49	Operation	operator: 51 operands: 52
50	ExprTuple	53, 54
51	Literal
52	ExprTuple	60, 55
53	Operation	operator: 56 operand: 60
54	Operation	operator: 58 operands: 59
55	Literal
56	Variable
57	ExprTuple	60
58	Literal
59	ExprTuple	61, 62
60	Variable
61	Literal
62	Literal