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, n
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
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [K], instance_expr = 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))), InSet(n, NaturalPos))))

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 \mapsto \left\{\forall_{K}~\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] \textrm{ if } n \in \mathbb{N}^+\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: 57 body: 3
2	ExprTuple	57
3	Conditional	value: 4 condition: 5
4	Operation	operator: 30 operand: 8
5	Operation	operator: 58 operands: 7
6	ExprTuple	8
7	ExprTuple	57, 9
8	Lambda	parameter: 49 body: 10
9	Literal
10	Operation	operator: 30 operand: 12
11	ExprTuple	12
12	Lambda	parameter: 61 body: 14
13	ExprTuple	61
14	Conditional	value: 15 condition: 16
15	Operation	operator: 30 operand: 20
16	Operation	operator: 18 operands: 19
17	ExprTuple	20
18	Literal
19	ExprTuple	61, 21
20	Lambda	parameters: 22 body: 23
21	Operation	operator: 24 operand: 49
22	ExprTuple	26
23	Conditional	value: 27 condition: 28
24	Literal
25	ExprTuple	49
26	ExprRange	lambda_map: 29 start_index: 56 end_index: 57
27	Operation	operator: 30 operand: 33
28	Operation	operator: 44 operands: 32
29	Lambda	parameter: 69 body: 64
30	Literal
31	ExprTuple	33
32	ExprTuple	34
33	Lambda	parameters: 35 body: 36
34	ExprRange	lambda_map: 37 start_index: 56 end_index: 57
35	ExprTuple	38
36	Conditional	value: 39 condition: 40
37	Lambda	parameter: 69 body: 41
38	ExprRange	lambda_map: 42 start_index: 56 end_index: 57
39	Operation	operator: 58 operands: 43
40	Operation	operator: 44 operands: 45
41	Operation	operator: 58 operands: 46
42	Lambda	parameter: 69 body: 65
43	ExprTuple	47, 61
44	Literal
45	ExprTuple	48
46	ExprTuple	64, 49
47	Operation	operator: 50 operands: 51
48	ExprRange	lambda_map: 52 start_index: 56 end_index: 57
49	Variable
50	Literal
51	ExprTuple	53
52	Lambda	parameter: 69 body: 54
53	ExprRange	lambda_map: 55 start_index: 56 end_index: 57
54	Operation	operator: 58 operands: 59
55	Lambda	parameter: 69 body: 60
56	Literal
57	Variable
58	Literal
59	ExprTuple	65, 61
60	Operation	operator: 62 operands: 63
61	Variable
62	Literal
63	ExprTuple	64, 65
64	IndexedVar	variable: 66 index: 69
65	IndexedVar	variable: 67 index: 69
66	Variable
67	Variable
68	ExprTuple	69
69	Variable