Expression of type Conditional ¶

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, V, Variable, a, n, x
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import ScalarMult, VecAdd, VecSpaces
from proveit.logic import Equals, Forall, InClass
from proveit.numbers import Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Forall(instance_param_or_params = [n], instance_expr = 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), domain = Natural), InClass(V, VecSpaces(K)))

# 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())

\left\{\forall_{n \in \mathbb{N}}~\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]\right] \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 22 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	50, 7
6	Lambda	parameter: 53 body: 9
7	Operation	operator: 10 operand: 26
8	ExprTuple	53
9	Conditional	value: 12 condition: 13
10	Literal
11	ExprTuple	26
12	Operation	operator: 22 operand: 16
13	Operation	operator: 46 operands: 15
14	ExprTuple	16
15	ExprTuple	53, 17
16	Lambda	parameter: 56 body: 19
17	Literal
18	ExprTuple	56
19	Conditional	value: 20 condition: 21
20	Operation	operator: 22 operand: 25
21	Operation	operator: 46 operands: 24
22	Literal
23	ExprTuple	25
24	ExprTuple	56, 26
25	Lambda	parameters: 44 body: 27
26	Variable
27	Conditional	value: 28 condition: 29
28	Operation	operator: 30 operands: 31
29	Operation	operator: 32 operands: 33
30	Literal
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	36
34	Operation	operator: 54 operands: 37
35	Operation	operator: 43 operands: 38
36	ExprRange	lambda_map: 39 start_index: 52 end_index: 53
37	ExprTuple	56, 40
38	ExprTuple	41
39	Lambda	parameter: 60 body: 42
40	Operation	operator: 43 operands: 44
41	ExprRange	lambda_map: 45 start_index: 52 end_index: 53
42	Operation	operator: 46 operands: 47
43	Literal
44	ExprTuple	48
45	Lambda	parameter: 60 body: 49
46	Literal
47	ExprTuple	57, 50
48	ExprRange	lambda_map: 51 start_index: 52 end_index: 53
49	Operation	operator: 54 operands: 55
50	Variable
51	Lambda	parameter: 60 body: 57
52	Literal
53	Variable
54	Literal
55	ExprTuple	56, 57
56	Variable
57	IndexedVar	variable: 58 index: 60
58	Variable
59	ExprTuple	60
60	Variable

Expression of type Conditional¶

from the theory of proveit.linear_algebra.scalar_multiplication¶

Expression of type Conditional ¶

from the theory of proveit.linear_algebra.scalar_multiplication ¶