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, a, x, y
from proveit.linear_algebra import InnerProd, ScalarMult
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(InnerProd(ScalarMult(a, x), y), ScalarMult(a, InnerProd(x, y))), domain = H), InSet(a, 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 \in H}~\left(\left \langle a \cdot x, y\right \rangle = \left(a \cdot \left \langle x, y\right \rangle\right)\right) \textrm{ if } a \in K\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: 22 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	31, 7
6	Lambda	parameters: 30 body: 8
7	Variable
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17, 18
15	Operation	operator: 29 operands: 19
16	Operation	operator: 27 operands: 20
17	Operation	operator: 22 operands: 21
18	Operation	operator: 22 operands: 23
19	ExprTuple	24, 33
20	ExprTuple	31, 25
21	ExprTuple	32, 26
22	Literal
23	ExprTuple	33, 26
24	Operation	operator: 27 operands: 28
25	Operation	operator: 29 operands: 30
26	Variable
27	Literal
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	32, 33
31	Variable
32	Variable
33	Variable