Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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(\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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	31, 30, 32
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13, 14
10	Operation	operator: 28 operands: 15
11	Operation	operator: 25 operands: 16
12	Operation	operator: 19 operands: 17
13	Operation	operator: 19 operands: 18
14	Operation	operator: 19 operands: 20
15	ExprTuple	31, 21
16	ExprTuple	22, 23
17	ExprTuple	31, 24
18	ExprTuple	30, 24
19	Literal
20	ExprTuple	32, 24
21	Operation	operator: 25 operands: 26
22	Operation	operator: 28 operands: 27
23	Operation	operator: 28 operands: 29
24	Variable
25	Literal
26	ExprTuple	30, 32
27	ExprTuple	31, 30
28	Literal
29	ExprTuple	31, 32
30	Variable
31	Variable
32	Variable