Expression of type Lambda

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, Lambda, V
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import VecAdd, VecSpaces
from proveit.logic import Forall, InClass, InSet

# build up the expression from sub-expressions
expr = Lambda(V, Conditional(Forall(instance_param_or_params = [x_1_to_n], instance_expr = InSet(VecAdd(x_1_to_n), V), domain = V), 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_{x_{1}, x_{2}, \ldots, x_{n} \in V}~\left(\left(x_{1} +  x_{2} +  \ldots +  x_{n}\right) \in V\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: 33 body: 2
1	ExprTuple	33
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	33, 10
9	Lambda	parameters: 23 body: 11
10	Operation	operator: 12 operand: 16
11	Conditional	value: 14 condition: 15
12	Literal
13	ExprTuple	16
14	Operation	operator: 30 operands: 17
15	Operation	operator: 18 operands: 19
16	Variable
17	ExprTuple	20, 33
18	Literal
19	ExprTuple	21
20	Operation	operator: 22 operands: 23
21	ExprRange	lambda_map: 24 start_index: 28 end_index: 29
22	Literal
23	ExprTuple	25
24	Lambda	parameter: 36 body: 26
25	ExprRange	lambda_map: 27 start_index: 28 end_index: 29
26	Operation	operator: 30 operands: 31
27	Lambda	parameter: 36 body: 32
28	Literal
29	Variable
30	Literal
31	ExprTuple	32, 33
32	IndexedVar	variable: 34 index: 36
33	Variable
34	Variable
35	ExprTuple	36
36	Variable