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, Py, V, x, y
from proveit.linear_algebra import VecAdd
from proveit.logic import And, Equals, InSet

# build up the expression from sub-expressions
expr = Conditional(Equals(Function(P, [VecAdd(x, y)]), VecAdd(Px, Py)), And(InSet(x, V), InSet(y, V)))

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\left(x + y\right) = \left(P\left(x\right) + P\left(y\right)\right) \textrm{ if } x \in V ,  y \in V\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 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 23 operand: 16
8	Operation	operator: 20 operands: 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprTuple	16
12	ExprTuple	17, 18
13	ExprTuple	25, 19
14	Literal
15	ExprTuple	26, 19
16	Operation	operator: 20 operands: 21
17	Operation	operator: 23 operand: 25
18	Operation	operator: 23 operand: 26
19	Variable
20	Literal
21	ExprTuple	25, 26
22	ExprTuple	25
23	Variable
24	ExprTuple	26
25	Variable
26	Variable