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