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, Lambda, X, x, y
from proveit.linear_algebra import InnerProd
from proveit.logic import Equals, InSet
from proveit.numbers import zero

# build up the expression from sub-expressions
expr = Lambda(x, Conditional(Equals(InnerProd(x, y), zero), InSet(x, X)))

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())

x \mapsto \left\{\left \langle x, y\right \rangle = 0 \textrm{ if } x \in X\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 14 body: 2
1	ExprTuple	14
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	14, 11
9	Operation	operator: 12 operands: 13
10	Literal
11	Variable
12	Literal
13	ExprTuple	14, 15
14	Variable
15	Variable