Expression of type Conditional

from the theory of proveit.linear_algebra.vector_sets

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 Bases, Dim, VecSpaces
from proveit.logic import Equals, Forall, InClass, InSet, Set
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [x_1_to_n], instance_expr = Equals(Dim(V), n), condition = InSet(Set(x_1_to_n), Bases(V))), domain = NaturalPos), 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\{\forall_{n \in \mathbb{N}^+}~\left[\forall_{x_{1}, x_{2}, \ldots, x_{n}~|~\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{Bases}\left(V\right)}~\left(\textrm{Dim}\left(V\right) = n\right)\right] \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\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: 15 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	36, 7
6	Lambda	parameter: 39 body: 9
7	Operation	operator: 10 operand: 14
8	ExprTuple	39
9	Conditional	value: 12 condition: 13
10	Literal
11	ExprTuple	14
12	Operation	operator: 15 operand: 18
13	Operation	operator: 25 operands: 17
14	Variable
15	Literal
16	ExprTuple	18
17	ExprTuple	39, 19
18	Lambda	parameters: 32 body: 20
19	Literal
20	Conditional	value: 21 condition: 22
21	Operation	operator: 23 operands: 24
22	Operation	operator: 25 operands: 26
23	Literal
24	ExprTuple	27, 39
25	Literal
26	ExprTuple	28, 29
27	Operation	operator: 30 operand: 36
28	Operation	operator: 31 operands: 32
29	Operation	operator: 33 operand: 36
30	Literal
31	Literal
32	ExprTuple	35
33	Literal
34	ExprTuple	36
35	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
36	Variable
37	Lambda	parameter: 43 body: 40
38	Literal
39	Variable
40	IndexedVar	variable: 41 index: 43
41	Variable
42	ExprTuple	43
43	Variable