Expression of type ExprTuple

from the theory of proveit.linear_algebra.scalar_multiplication

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 a_1_to_n, x_1_to_n
from proveit.linear_algebra import VecSpaces, lin_comb_axn
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 = [a_1_to_n], instance_expr = Forall(instance_param_or_params = [x_1_to_n], instance_expr = InSet(lin_comb_axn, V), domain = V), domain = K), 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_{a_{1}, a_{2}, \ldots, a_{n} \in K}~\left[\forall_{x_{1}, x_{2}, \ldots, x_{n} \in V}~\left(\left(\left(a_{1} \cdot x_{1}\right) +  \left(a_{2} \cdot x_{2}\right) +  \ldots +  \left(a_{n} \cdot x_{n}\right)\right) \in V\right)\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: 41 body: 2
2	Operation	operator: 22 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 53 body: 6
5	ExprTuple	53
6	Conditional	value: 7 condition: 8
7	Operation	operator: 22 operand: 12
8	Operation	operator: 10 operands: 11
9	ExprTuple	12
10	Literal
11	ExprTuple	53, 13
12	Lambda	parameters: 14 body: 15
13	Operation	operator: 16 operand: 41
14	ExprTuple	18
15	Conditional	value: 19 condition: 20
16	Literal
17	ExprTuple	41
18	ExprRange	lambda_map: 21 start_index: 48 end_index: 49
19	Operation	operator: 22 operand: 25
20	Operation	operator: 36 operands: 24
21	Lambda	parameter: 61 body: 56
22	Literal
23	ExprTuple	25
24	ExprTuple	26
25	Lambda	parameters: 27 body: 28
26	ExprRange	lambda_map: 29 start_index: 48 end_index: 49
27	ExprTuple	30
28	Conditional	value: 31 condition: 32
29	Lambda	parameter: 61 body: 33
30	ExprRange	lambda_map: 34 start_index: 48 end_index: 49
31	Operation	operator: 50 operands: 35
32	Operation	operator: 36 operands: 37
33	Operation	operator: 50 operands: 38
34	Lambda	parameter: 61 body: 57
35	ExprTuple	39, 53
36	Literal
37	ExprTuple	40
38	ExprTuple	56, 41
39	Operation	operator: 42 operands: 43
40	ExprRange	lambda_map: 44 start_index: 48 end_index: 49
41	Variable
42	Literal
43	ExprTuple	45
44	Lambda	parameter: 61 body: 46
45	ExprRange	lambda_map: 47 start_index: 48 end_index: 49
46	Operation	operator: 50 operands: 51
47	Lambda	parameter: 61 body: 52
48	Literal
49	Variable
50	Literal
51	ExprTuple	57, 53
52	Operation	operator: 54 operands: 55
53	Variable
54	Literal
55	ExprTuple	56, 57
56	IndexedVar	variable: 58 index: 61
57	IndexedVar	variable: 59 index: 61
58	Variable
59	Variable
60	ExprTuple	61
61	Variable