Axiom lin_map_def of type Forall

from the theory of proveit.linear_algebra.linear_maps

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_axiom_expr # Load the stored axiom expression as 'stored_expr'
# import the special expression
from proveit.linear_algebra.linear_maps import lin_map_def

# check that the built expression is the same as the stored expression
assert lin_map_def.expr == stored_expr
assert lin_map_def.expr._style_id == stored_expr._style_id
print("Passed sanity check: lin_map_def matches stored_expr")

Passed sanity check: lin_map_def matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{K}~\left[\forall_{V, W \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{P}~\left(\begin{array}{c} \begin{array}{l} \left(P \in \mathcal{L}\left(V, W\right)\right) \Leftrightarrow  \\ \left(\begin{array}{c} \left[\forall_{x \in V}~\left(P\left(x\right) \in W\right)\right] \land  \\ \left[\forall_{x, y \in V}~\left(P\left(x + y\right) = \left(P\left(x\right) + P\left(y\right)\right)\right)\right] \land  \\ \left[\forall_{c \in K}~\left[\forall_{x \in V}~\left(P\left(c \cdot x\right) = \left(c \cdot P\left(x\right)\right)\right)\right]\right] \end{array}\right) \end{array} \end{array}\right)\right]\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 53 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 61 body: 3
3	Operation	operator: 53 operand: 5
4	ExprTuple	5
5	Lambda	parameters: 33 body: 6
6	Conditional	value: 7 condition: 8
7	Operation	operator: 53 operand: 11
8	Operation	operator: 51 operands: 10
9	ExprTuple	11
10	ExprTuple	12, 13
11	Lambda	parameter: 87 body: 15
12	Operation	operator: 17 operands: 16
13	Operation	operator: 17 operands: 18
14	ExprTuple	87
15	Operation	operator: 19 operands: 20
16	ExprTuple	80, 21
17	Literal
18	ExprTuple	56, 21
19	Literal
20	ExprTuple	22, 23
21	Operation	operator: 24 operand: 61
22	Operation	operator: 75 operands: 26
23	Operation	operator: 51 operands: 27
24	Literal
25	ExprTuple	61
26	ExprTuple	87, 28
27	ExprTuple	29, 30, 31
28	Operation	operator: 32 operands: 33
29	Operation	operator: 53 operand: 37
30	Operation	operator: 53 operand: 38
31	Operation	operator: 53 operand: 39
32	Literal
33	ExprTuple	80, 56
34	ExprTuple	37
35	ExprTuple	38
36	ExprTuple	39
37	Lambda	parameter: 90 body: 40
38	Lambda	parameters: 71 body: 41
39	Lambda	parameter: 89 body: 43
40	Conditional	value: 44 condition: 69
41	Conditional	value: 45 condition: 46
42	ExprTuple	89
43	Conditional	value: 47 condition: 48
44	Operation	operator: 75 operands: 49
45	Operation	operator: 73 operands: 50
46	Operation	operator: 51 operands: 52
47	Operation	operator: 53 operand: 60
48	Operation	operator: 75 operands: 55
49	ExprTuple	84, 56
50	ExprTuple	57, 58
51	Literal
52	ExprTuple	69, 59
53	Literal
54	ExprTuple	60
55	ExprTuple	89, 61
56	Variable
57	Operation	operator: 87 operand: 66
58	Operation	operator: 70 operands: 63
59	Operation	operator: 75 operands: 64
60	Lambda	parameter: 90 body: 65
61	Variable
62	ExprTuple	66
63	ExprTuple	84, 67
64	ExprTuple	77, 80
65	Conditional	value: 68 condition: 69
66	Operation	operator: 70 operands: 71
67	Operation	operator: 87 operand: 77
68	Operation	operator: 73 operands: 74
69	Operation	operator: 75 operands: 76
70	Literal
71	ExprTuple	90, 77
72	ExprTuple	77
73	Literal
74	ExprTuple	78, 79
75	Literal
76	ExprTuple	90, 80
77	Variable
78	Operation	operator: 87 operand: 83
79	Operation	operator: 85 operands: 82
80	Variable
81	ExprTuple	83
82	ExprTuple	89, 84
83	Operation	operator: 85 operands: 86
84	Operation	operator: 87 operand: 90
85	Literal
86	ExprTuple	89, 90
87	Variable
88	ExprTuple	90
89	Variable
90	Variable