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, K, x, y, z
from proveit.linear_algebra import InnerProd, InnerProdSpaces, VecAdd
from proveit.logic import Equals, Forall, InClass

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [x, y, z], instance_expr = Equals(InnerProd(x, VecAdd(y, z)), VecAdd(InnerProd(x, y), InnerProd(x, z))), domain = H), InClass(H, InnerProdSpaces(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, y, z \in H}~\left(\left \langle x, y + z\right \rangle = \left(\left \langle x, y\right \rangle + \left \langle x, z\right \rangle\right)\right) \textrm{ if } H \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(K\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: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	34, 8
7	Lambda	parameters: 9 body: 10
8	Operation	operator: 11 operand: 15
9	ExprTuple	41, 40, 42
10	Conditional	value: 13 condition: 14
11	Literal
12	ExprTuple	15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	Variable
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22, 23, 24
20	Operation	operator: 38 operands: 25
21	Operation	operator: 35 operands: 26
22	Operation	operator: 29 operands: 27
23	Operation	operator: 29 operands: 28
24	Operation	operator: 29 operands: 30
25	ExprTuple	41, 31
26	ExprTuple	32, 33
27	ExprTuple	41, 34
28	ExprTuple	40, 34
29	Literal
30	ExprTuple	42, 34
31	Operation	operator: 35 operands: 36
32	Operation	operator: 38 operands: 37
33	Operation	operator: 38 operands: 39
34	Variable
35	Literal
36	ExprTuple	40, 42
37	ExprTuple	41, 40
38	Literal
39	ExprTuple	41, 42
40	Variable
41	Variable
42	Variable