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
from proveit.logic import And, Equals, Forall, Iff, InSet

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(Lambda(P, 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)))

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(P \mapsto \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)

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: 69 body: 3
2	ExprTuple	69
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 57 operands: 8
7	Operation	operator: 33 operands: 9
8	ExprTuple	69, 10
9	ExprTuple	11, 12, 13
10	Operation	operator: 14 operands: 15
11	Operation	operator: 35 operand: 19
12	Operation	operator: 35 operand: 20
13	Operation	operator: 35 operand: 21
14	Literal
15	ExprTuple	62, 38
16	ExprTuple	19
17	ExprTuple	20
18	ExprTuple	21
19	Lambda	parameter: 72 body: 22
20	Lambda	parameters: 53 body: 23
21	Lambda	parameter: 71 body: 25
22	Conditional	value: 26 condition: 51
23	Conditional	value: 27 condition: 28
24	ExprTuple	71
25	Conditional	value: 29 condition: 30
26	Operation	operator: 57 operands: 31
27	Operation	operator: 55 operands: 32
28	Operation	operator: 33 operands: 34
29	Operation	operator: 35 operand: 42
30	Operation	operator: 57 operands: 37
31	ExprTuple	66, 38
32	ExprTuple	39, 40
33	Literal
34	ExprTuple	51, 41
35	Literal
36	ExprTuple	42
37	ExprTuple	71, 43
38	Variable
39	Operation	operator: 69 operand: 48
40	Operation	operator: 52 operands: 45
41	Operation	operator: 57 operands: 46
42	Lambda	parameter: 72 body: 47
43	Variable
44	ExprTuple	48
45	ExprTuple	66, 49
46	ExprTuple	59, 62
47	Conditional	value: 50 condition: 51
48	Operation	operator: 52 operands: 53
49	Operation	operator: 69 operand: 59
50	Operation	operator: 55 operands: 56
51	Operation	operator: 57 operands: 58
52	Literal
53	ExprTuple	72, 59
54	ExprTuple	59
55	Literal
56	ExprTuple	60, 61
57	Literal
58	ExprTuple	72, 62
59	Variable
60	Operation	operator: 69 operand: 65
61	Operation	operator: 67 operands: 64
62	Variable
63	ExprTuple	65
64	ExprTuple	71, 66
65	Operation	operator: 67 operands: 68
66	Operation	operator: 69 operand: 72
67	Literal
68	ExprTuple	71, 72
69	Variable
70	ExprTuple	72
71	Variable
72	Variable