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, Lambda, Py, X, x, y
from proveit.linear_algebra import Hspace, InnerProd, VecZero
from proveit.logic import Equals, Forall, Implies, InSet
from proveit.numbers import zero

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(y, Conditional(Implies(Forall(instance_param_or_params = [x], instance_expr = Equals(InnerProd(x, y), zero), domain = X), Equals(Py, VecZero(Hspace))), InSet(y, Hspace))))

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(y \mapsto \left\{\left[\forall_{x \in X}~\left(\left \langle x, y\right \rangle = 0\right)\right] \Rightarrow \left(P\left(y\right) = \vec{0}\left(\mathcal{H}\right)\right) \textrm{ if } y \in \mathcal{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	parameter: 35 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 27 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	35, 24
8	Operation	operator: 10 operand: 13
9	Operation	operator: 25 operands: 12
10	Literal
11	ExprTuple	13
12	ExprTuple	14, 15
13	Lambda	parameter: 34 body: 17
14	Operation	operator: 18 operand: 35
15	Operation	operator: 20 operand: 24
16	ExprTuple	34
17	Conditional	value: 22 condition: 23
18	Variable
19	ExprTuple	35
20	Literal
21	ExprTuple	24
22	Operation	operator: 25 operands: 26
23	Operation	operator: 27 operands: 28
24	Variable
25	Literal
26	ExprTuple	29, 30
27	Literal
28	ExprTuple	34, 31
29	Operation	operator: 32 operands: 33
30	Literal
31	Variable
32	Literal
33	ExprTuple	34, 35
34	Variable
35	Variable