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, a, x, y
from proveit.linear_algebra import InnerProd, ScalarMult
from proveit.logic import And, Equals, InSet

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([x, y], Conditional(Equals(InnerProd(ScalarMult(a, x), y), ScalarMult(a, InnerProd(x, y))), And(InSet(x, H), InSet(y, 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\right) \mapsto \left\{\left \langle a \cdot x, y\right \rangle = \left(a \cdot \left \langle x, y\right \rangle\right) \textrm{ if } x \in H ,  y \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: 24 body: 2
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
9	Operation	operator: 23 operands: 13
10	Operation	operator: 21 operands: 14
11	Operation	operator: 16 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprTuple	18, 27
14	ExprTuple	25, 19
15	ExprTuple	26, 20
16	Literal
17	ExprTuple	27, 20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	Variable
21	Literal
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	26, 27
25	Variable
26	Variable
27	Variable