Expression of type ExprTuple

from the theory of proveit.linear_algebra.linear_maps

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 ExprTuple, Function, K, Lambda, P, Px, Py, V, W, c, x, y
from proveit.linear_algebra import LinMap, ScalarMult, VecAdd, VecSpaces
from proveit.logic import And, Equals, Forall, Iff, InSet

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(Lambda(K, Forall(instance_param_or_params = [V, W], instance_expr = Forall(instance_param_or_params = [P], instance_expr = Iff(InSet(P, LinMap(V, W)), And(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(Px, W), domain = V), Forall(instance_param_or_params = [x, y], instance_expr = Equals(Function(P, [VecAdd(x, y)]), VecAdd(Px, Py)), domain = V), Forall(instance_param_or_params = [c], instance_expr = Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Function(P, [ScalarMult(c, x)]), ScalarMult(c, Px)), domain = V), domain = K)).with_wrapping_at(2,4)).with_wrapping_at(2)), domain = VecSpaces(K))))

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())

\left(K \mapsto \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]\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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