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, K, Lambda, V
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import VecAdd, VecSpaces
from proveit.logic import Forall, InSet

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(K, Forall(instance_param_or_params = [V], instance_expr = Forall(instance_param_or_params = [x_1_to_n], instance_expr = InSet(VecAdd(x_1_to_n), V), domain = V), domain = VecSpaces(K))))

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(K \mapsto \left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{x_{1}, x_{2}, \ldots, x_{n} \in V}~\left(\left(x_{1} +  x_{2} +  \ldots +  x_{n}\right) \in V\right)\right]\right]\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 20 body: 2
2	Operation	operator: 9 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 37 body: 6
5	ExprTuple	37
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operand: 13
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13
11	Literal
12	ExprTuple	37, 14
13	Lambda	parameters: 27 body: 15
14	Operation	operator: 16 operand: 20
15	Conditional	value: 18 condition: 19
16	Literal
17	ExprTuple	20
18	Operation	operator: 34 operands: 21
19	Operation	operator: 22 operands: 23
20	Variable
21	ExprTuple	24, 37
22	Literal
23	ExprTuple	25
24	Operation	operator: 26 operands: 27
25	ExprRange	lambda_map: 28 start_index: 32 end_index: 33
26	Literal
27	ExprTuple	29
28	Lambda	parameter: 40 body: 30
29	ExprRange	lambda_map: 31 start_index: 32 end_index: 33
30	Operation	operator: 34 operands: 35
31	Lambda	parameter: 40 body: 36
32	Literal
33	Variable
34	Literal
35	ExprTuple	36, 37
36	IndexedVar	variable: 38 index: 40
37	Variable
38	Variable
39	ExprTuple	40
40	Variable