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, K, V
from proveit.core_expr_types import a_1_to_n, x_1_to_n
from proveit.linear_algebra import VecSpaces, lin_comb_axn
from proveit.logic import Forall, InClass, InSet

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_n], instance_expr = Forall(instance_param_or_params = [x_1_to_n], instance_expr = InSet(lin_comb_axn, V), domain = V), domain = K), 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_{a_{1}, a_{2}, \ldots, a_{n} \in K}~\left[\forall_{x_{1}, x_{2}, \ldots, x_{n} \in V}~\left(\left(\left(a_{1} \cdot x_{1}\right) +  \left(a_{2} \cdot x_{2}\right) +  \ldots +  \left(a_{n} \cdot x_{n}\right)\right) \in V\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: 16 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	47, 7
6	Lambda	parameters: 8 body: 9
7	Operation	operator: 10 operand: 35
8	ExprTuple	12
9	Conditional	value: 13 condition: 14
10	Literal
11	ExprTuple	35
12	ExprRange	lambda_map: 15 start_index: 42 end_index: 43
13	Operation	operator: 16 operand: 19
14	Operation	operator: 30 operands: 18
15	Lambda	parameter: 55 body: 50
16	Literal
17	ExprTuple	19
18	ExprTuple	20
19	Lambda	parameters: 21 body: 22
20	ExprRange	lambda_map: 23 start_index: 42 end_index: 43
21	ExprTuple	24
22	Conditional	value: 25 condition: 26
23	Lambda	parameter: 55 body: 27
24	ExprRange	lambda_map: 28 start_index: 42 end_index: 43
25	Operation	operator: 44 operands: 29
26	Operation	operator: 30 operands: 31
27	Operation	operator: 44 operands: 32
28	Lambda	parameter: 55 body: 51
29	ExprTuple	33, 47
30	Literal
31	ExprTuple	34
32	ExprTuple	50, 35
33	Operation	operator: 36 operands: 37
34	ExprRange	lambda_map: 38 start_index: 42 end_index: 43
35	Variable
36	Literal
37	ExprTuple	39
38	Lambda	parameter: 55 body: 40
39	ExprRange	lambda_map: 41 start_index: 42 end_index: 43
40	Operation	operator: 44 operands: 45
41	Lambda	parameter: 55 body: 46
42	Literal
43	Variable
44	Literal
45	ExprTuple	51, 47
46	Operation	operator: 48 operands: 49
47	Variable
48	Literal
49	ExprTuple	50, 51
50	IndexedVar	variable: 52 index: 55
51	IndexedVar	variable: 53 index: 55
52	Variable
53	Variable
54	ExprTuple	55
55	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 ¶