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, Lambda, V, n
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import Bases, Dim
from proveit.logic import Equals, Forall, InSet, Set
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [x_1_to_n], instance_expr = Equals(Dim(V), n), condition = InSet(Set(x_1_to_n), Bases(V))), 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())

n \mapsto \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) \textrm{ if } n \in \mathbb{N}^+\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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