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 Conditional, 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, InClass, InSet

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(V, Conditional(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), InClass(V, 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(V \mapsto \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] \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\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: 50 body: 3
2	ExprTuple	50
3	Conditional	value: 4 condition: 5
4	Operation	operator: 19 operand: 9
5	Operation	operator: 7 operands: 8
6	ExprTuple	9
7	Literal
8	ExprTuple	50, 10
9	Lambda	parameters: 11 body: 12
10	Operation	operator: 13 operand: 38
11	ExprTuple	15
12	Conditional	value: 16 condition: 17
13	Literal
14	ExprTuple	38
15	ExprRange	lambda_map: 18 start_index: 45 end_index: 46
16	Operation	operator: 19 operand: 22
17	Operation	operator: 33 operands: 21
18	Lambda	parameter: 58 body: 53
19	Literal
20	ExprTuple	22
21	ExprTuple	23
22	Lambda	parameters: 24 body: 25
23	ExprRange	lambda_map: 26 start_index: 45 end_index: 46
24	ExprTuple	27
25	Conditional	value: 28 condition: 29
26	Lambda	parameter: 58 body: 30
27	ExprRange	lambda_map: 31 start_index: 45 end_index: 46
28	Operation	operator: 47 operands: 32
29	Operation	operator: 33 operands: 34
30	Operation	operator: 47 operands: 35
31	Lambda	parameter: 58 body: 54
32	ExprTuple	36, 50
33	Literal
34	ExprTuple	37
35	ExprTuple	53, 38
36	Operation	operator: 39 operands: 40
37	ExprRange	lambda_map: 41 start_index: 45 end_index: 46
38	Variable
39	Literal
40	ExprTuple	42
41	Lambda	parameter: 58 body: 43
42	ExprRange	lambda_map: 44 start_index: 45 end_index: 46
43	Operation	operator: 47 operands: 48
44	Lambda	parameter: 58 body: 49
45	Literal
46	Variable
47	Literal
48	ExprTuple	54, 50
49	Operation	operator: 51 operands: 52
50	Variable
51	Literal
52	ExprTuple	53, 54
53	IndexedVar	variable: 55 index: 58
54	IndexedVar	variable: 56 index: 58
55	Variable
56	Variable
57	ExprTuple	58
58	Variable