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 ScalarMult, VecAdd
from proveit.logic import Equals, Forall, InSet

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

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(\forall_{x \in V}~\left(P\left(x\right) \in W\right), \forall_{x, y \in V}~\left(P\left(x + y\right) = \left(P\left(x\right) + P\left(y\right)\right)\right), \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)

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