Expression of type Conditional

from the theory of proveit.linear_algebra.inner_products

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, H, x, y, z
from proveit.linear_algebra import InnerProd, VecAdd
from proveit.logic import And, Equals, InSet

# build up the expression from sub-expressions
expr = Conditional(Equals(InnerProd(x, VecAdd(y, z)), VecAdd(InnerProd(x, y), InnerProd(x, z))), And(InSet(x, H), InSet(y, H), InSet(z, H)))

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 \langle x, y + z\right \rangle = \left(\left \langle x, y\right \rangle + \left \langle x, z\right \rangle\right) \textrm{ if } x \in H ,  y \in H ,  z \in H\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, 11
7	Operation	operator: 25 operands: 12
8	Operation	operator: 22 operands: 13
9	Operation	operator: 16 operands: 14
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	ExprTuple	28, 18
13	ExprTuple	19, 20
14	ExprTuple	28, 21
15	ExprTuple	27, 21
16	Literal
17	ExprTuple	29, 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 25 operands: 24
20	Operation	operator: 25 operands: 26
21	Variable
22	Literal
23	ExprTuple	27, 29
24	ExprTuple	28, 27
25	Literal
26	ExprTuple	28, 29
27	Variable
28	Variable
29	Variable