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, 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 = Lambda(n, 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())

n \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 40 body: 2
1	ExprTuple	40
2	Conditional	value: 3 condition: 4
3	Operation	operator: 16 operand: 7
4	Operation	operator: 41 operands: 6
5	ExprTuple	7
6	ExprTuple	40, 8
7	Lambda	parameter: 27 body: 9
8	Literal
9	Operation	operator: 16 operand: 11
10	ExprTuple	11
11	Lambda	parameter: 44 body: 13
12	ExprTuple	44
13	Conditional	value: 14 condition: 15
14	Operation	operator: 16 operand: 20
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	20
18	Literal
19	ExprTuple	44, 21
20	Lambda	parameters: 34 body: 22
21	Operation	operator: 23 operand: 27
22	Conditional	value: 25 condition: 26
23	Literal
24	ExprTuple	27
25	Operation	operator: 41 operands: 28
26	Operation	operator: 29 operands: 30
27	Variable
28	ExprTuple	31, 44
29	Literal
30	ExprTuple	32
31	Operation	operator: 33 operands: 34
32	ExprRange	lambda_map: 35 start_index: 39 end_index: 40
33	Literal
34	ExprTuple	36
35	Lambda	parameter: 47 body: 37
36	ExprRange	lambda_map: 38 start_index: 39 end_index: 40
37	Operation	operator: 41 operands: 42
38	Lambda	parameter: 47 body: 43
39	Literal
40	Variable
41	Literal
42	ExprTuple	43, 44
43	IndexedVar	variable: 45 index: 47
44	Variable
45	Variable
46	ExprTuple	47
47	Variable