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, v
from proveit.core_expr_types import a_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_1_to_n], instance_expr = Forall(instance_param_or_params = [v], instance_expr = Equals(ScalarMult(VecAdd(a_1_to_n), v), VecAdd(ExprRange(sub_expr1, ScalarMult(IndexedVar(a, sub_expr1), v), 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_{1}, a_{2}, \ldots, a_{n} \in K}~\left[\forall_{v \in V}~\left(\begin{array}{c} \begin{array}{l} \left(\left(a_{1} +  a_{2} +  \ldots +  a_{n}\right) \cdot v\right) =  \\ \left(\left(a_{1} \cdot v\right) +  \left(a_{2} \cdot v\right) +  \ldots +  \left(a_{n} \cdot v\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: 21 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	40, 7
6	Lambda	parameter: 53 body: 9
7	Operation	operator: 10 operand: 41
8	ExprTuple	53
9	Conditional	value: 12 condition: 13
10	Literal
11	ExprTuple	41
12	Operation	operator: 21 operand: 16
13	Operation	operator: 36 operands: 15
14	ExprTuple	16
15	ExprTuple	53, 17
16	Lambda	parameters: 47 body: 18
17	Literal
18	Conditional	value: 19 condition: 20
19	Operation	operator: 21 operand: 25
20	Operation	operator: 23 operands: 24
21	Literal
22	ExprTuple	25
23	Literal
24	ExprTuple	26
25	Lambda	parameter: 57 body: 28
26	ExprRange	lambda_map: 29 start_index: 52 end_index: 53
27	ExprTuple	57
28	Conditional	value: 30 condition: 31
29	Lambda	parameter: 60 body: 32
30	Operation	operator: 33 operands: 34
31	Operation	operator: 36 operands: 35
32	Operation	operator: 36 operands: 37
33	Literal
34	ExprTuple	38, 39
35	ExprTuple	57, 40
36	Literal
37	ExprTuple	56, 41
38	Operation	operator: 54 operands: 42
39	Operation	operator: 46 operands: 43
40	Variable
41	Variable
42	ExprTuple	44, 57
43	ExprTuple	45
44	Operation	operator: 46 operands: 47
45	ExprRange	lambda_map: 48 start_index: 52 end_index: 53
46	Literal
47	ExprTuple	49
48	Lambda	parameter: 60 body: 50
49	ExprRange	lambda_map: 51 start_index: 52 end_index: 53
50	Operation	operator: 54 operands: 55
51	Lambda	parameter: 60 body: 56
52	Literal
53	Variable
54	Literal
55	ExprTuple	56, 57
56	IndexedVar	variable: 58 index: 60
57	Variable
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 ¶