Expression of type Lambda

from the theory of proveit.linear_algebra.scalar_multiplication

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, ExprRange, IndexedVar, K, Lambda, V, Variable, a, n, x
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [a], instance_expr = Forall(instance_param_or_params = [x_1_to_n], instance_expr = Equals(ScalarMult(a, VecAdd(x_1_to_n)), VecAdd(ExprRange(sub_expr1, ScalarMult(a, IndexedVar(x, sub_expr1)), one, n))).with_wrapping_at(2), domain = V), domain = K), InSet(n, Natural)))

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_{a \in K}~\left[\forall_{x_{1}, x_{2}, \ldots, x_{n} \in V}~\left(\begin{array}{c} \begin{array}{l} \left(a \cdot \left(x_{1} +  x_{2} +  \ldots +  x_{n}\right)\right) =  \\ \left(\left(a \cdot x_{1}\right) +  \left(a \cdot x_{2}\right) +  \ldots +  \left(a \cdot x_{n}\right)\right) \end{array} \end{array}\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: 44 body: 2
1	ExprTuple	44
2	Conditional	value: 3 condition: 4
3	Operation	operator: 13 operand: 7
4	Operation	operator: 37 operands: 6
5	ExprTuple	7
6	ExprTuple	44, 8
7	Lambda	parameter: 47 body: 10
8	Literal
9	ExprTuple	47
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operand: 16
12	Operation	operator: 37 operands: 15
13	Literal
14	ExprTuple	16
15	ExprTuple	47, 17
16	Lambda	parameters: 35 body: 18
17	Variable
18	Conditional	value: 19 condition: 20
19	Operation	operator: 21 operands: 22
20	Operation	operator: 23 operands: 24
21	Literal
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	27
25	Operation	operator: 45 operands: 28
26	Operation	operator: 34 operands: 29
27	ExprRange	lambda_map: 30 start_index: 43 end_index: 44
28	ExprTuple	47, 31
29	ExprTuple	32
30	Lambda	parameter: 51 body: 33
31	Operation	operator: 34 operands: 35
32	ExprRange	lambda_map: 36 start_index: 43 end_index: 44
33	Operation	operator: 37 operands: 38
34	Literal
35	ExprTuple	39
36	Lambda	parameter: 51 body: 40
37	Literal
38	ExprTuple	48, 41
39	ExprRange	lambda_map: 42 start_index: 43 end_index: 44
40	Operation	operator: 45 operands: 46
41	Variable
42	Lambda	parameter: 51 body: 48
43	Literal
44	Variable
45	Literal
46	ExprTuple	47, 48
47	Variable
48	IndexedVar	variable: 49 index: 51
49	Variable
50	ExprTuple	51
51	Variable