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, N, k, n, vk
from proveit.logic import CartExp, Forall, InSet
from proveit.numbers import Complex, Interval, Natural, NaturalPos, zero

# build up the expression from sub-expressions
expr = ExprTuple(InSet(n, NaturalPos), InSet(N, NaturalPos), Forall(instance_param_or_params = [k], instance_expr = InSet(vk, CartExp(Complex, n)), domain = Natural), InSet(k, Interval(zero, N)))

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(n \in \mathbb{N}^+, N \in \mathbb{N}^+, \forall_{k \in \mathbb{N}}~\left(v\left(k\right) \in \mathbb{C}^{n}\right), k \in \{0~\ldotp \ldotp~N\}\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
1	Operation	operator: 21 operands: 5
2	Operation	operator: 21 operands: 6
3	Operation	operator: 7 operand: 11
4	Operation	operator: 21 operands: 9
5	ExprTuple	32, 10
6	ExprTuple	19, 10
7	Literal
8	ExprTuple	11
9	ExprTuple	30, 12
10	Literal
11	Lambda	parameter: 30 body: 13
12	Operation	operator: 14 operands: 15
13	Conditional	value: 16 condition: 17
14	Literal
15	ExprTuple	18, 19
16	Operation	operator: 21 operands: 20
17	Operation	operator: 21 operands: 22
18	Literal
19	Variable
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	30, 25
23	Operation	operator: 26 operand: 30
24	Operation	operator: 28 operands: 29
25	Literal
26	Variable
27	ExprTuple	30
28	Literal
29	ExprTuple	31, 32
30	Variable
31	Literal
32	Variable