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, P, Px, Py, V, W, c, x, y
from proveit.linear_algebra import LinMap, ScalarMult, VecAdd
from proveit.logic import And, Equals, Forall, InSet

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

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 \in \mathcal{L}\left(V, W\right), \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)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

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