Expression of type Conditional

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, K, 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 = 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\{\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..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 14 operand: 5
2	Operation	operator: 39 operands: 4
3	ExprTuple	5
4	ExprTuple	38, 6
5	Lambda	parameter: 25 body: 7
6	Literal
7	Operation	operator: 14 operand: 9
8	ExprTuple	9
9	Lambda	parameter: 42 body: 11
10	ExprTuple	42
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operand: 18
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18
16	Literal
17	ExprTuple	42, 19
18	Lambda	parameters: 32 body: 20
19	Operation	operator: 21 operand: 25
20	Conditional	value: 23 condition: 24
21	Literal
22	ExprTuple	25
23	Operation	operator: 39 operands: 26
24	Operation	operator: 27 operands: 28
25	Variable
26	ExprTuple	29, 42
27	Literal
28	ExprTuple	30
29	Operation	operator: 31 operands: 32
30	ExprRange	lambda_map: 33 start_index: 37 end_index: 38
31	Literal
32	ExprTuple	34
33	Lambda	parameter: 45 body: 35
34	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
35	Operation	operator: 39 operands: 40
36	Lambda	parameter: 45 body: 41
37	Literal
38	Variable
39	Literal
40	ExprTuple	41, 42
41	IndexedVar	variable: 43 index: 45
42	Variable
43	Variable
44	ExprTuple	45
45	Variable