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 A, B, Conditional, Function, Lambda, V, W, x
from proveit.linear_algebra import LinMap, VecAdd
from proveit.logic import And, Equals, InSet

# build up the expression from sub-expressions
sub_expr1 = [x]
sub_expr2 = LinMap(V, W)
expr = Conditional(Equals(VecAdd(A, B), Lambda(x, Conditional(VecAdd(Function(A, sub_expr1), Function(B, sub_expr1)), InSet(x, V)))), And(InSet(A, sub_expr2), InSet(B, sub_expr2)))

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\{\left(A + B\right) = \left[x \mapsto \left\{A\left(x\right) + B\left(x\right) \textrm{ if } x \in V\right..\right] \textrm{ if } A \in \mathcal{L}\left(V, W\right) ,  B \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 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 18 operands: 11
8	Lambda	parameter: 31 body: 12
9	Operation	operator: 20 operands: 13
10	Operation	operator: 20 operands: 14
11	ExprTuple	28, 29
12	Conditional	value: 15 condition: 16
13	ExprTuple	28, 17
14	ExprTuple	29, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Operation	operator: 22 operands: 23
18	Literal
19	ExprTuple	24, 25
20	Literal
21	ExprTuple	31, 26
22	Literal
23	ExprTuple	26, 27
24	Operation	operator: 28 operand: 31
25	Operation	operator: 29 operand: 31
26	Variable
27	Variable
28	Variable
29	Variable
30	ExprTuple	31
31	Variable