Expression of type Lambda

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, Lambda, 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 = Lambda([x, y, z], 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(x, y, z\right) \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	30, 29, 31
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13
9	Operation	operator: 27 operands: 14
10	Operation	operator: 24 operands: 15
11	Operation	operator: 18 operands: 16
12	Operation	operator: 18 operands: 17
13	Operation	operator: 18 operands: 19
14	ExprTuple	30, 20
15	ExprTuple	21, 22
16	ExprTuple	30, 23
17	ExprTuple	29, 23
18	Literal
19	ExprTuple	31, 23
20	Operation	operator: 24 operands: 25
21	Operation	operator: 27 operands: 26
22	Operation	operator: 27 operands: 28
23	Variable
24	Literal
25	ExprTuple	29, 31
26	ExprTuple	30, 29
27	Literal
28	ExprTuple	30, 31
29	Variable
30	Variable
31	Variable