Expression of type Lambda

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, Lambda, 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 = Lambda(V, 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())

V \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

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