Expression of type Conditional

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 Conditional, Function, P, Px, V, W, x, y
from proveit.linear_algebra import LinMap, VecAdd
from proveit.logic import Equals, Forall, InSet

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [x, y], instance_expr = Equals(Function(P, [VecAdd(x, y)]), VecAdd(Px, Function(P, [y]))), domain = V), InSet(P, LinMap(V, W)))

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, y \in V}~\left(P\left(x + y\right) = \left(P\left(x\right) + P\left(y\right)\right)\right) \textrm{ if } P \in \mathcal{L}\left(V, W\right)\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 25 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	34, 7
6	Lambda	parameters: 32 body: 8
7	Operation	operator: 9 operands: 10
8	Conditional	value: 11 condition: 12
9	Literal
10	ExprTuple	30, 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	Variable
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21
18	Operation	operator: 34 operand: 27
19	Operation	operator: 31 operands: 23
20	Operation	operator: 25 operands: 24
21	Operation	operator: 25 operands: 26
22	ExprTuple	27
23	ExprTuple	28, 29
24	ExprTuple	36, 30
25	Literal
26	ExprTuple	37, 30
27	Operation	operator: 31 operands: 32
28	Operation	operator: 34 operand: 36
29	Operation	operator: 34 operand: 37
30	Variable
31	Literal
32	ExprTuple	36, 37
33	ExprTuple	36
34	Variable
35	ExprTuple	37
36	Variable
37	Variable