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

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Px, x), domain = X), Forall(instance_param_or_params = [y], instance_expr = Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(InnerProd(x, y), zero), domain = X), Equals(Py, VecZero(Hspace))), domain = 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(\forall_{x \in X}~\left(P\left(x\right) = x\right), \forall_{y \in \mathcal{H}}~\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)\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 19 operand: 5
2	Operation	operator: 19 operand: 6
3	ExprTuple	5
4	ExprTuple	6
5	Lambda	parameter: 43 body: 7
6	Lambda	parameter: 44 body: 8
7	Conditional	value: 9 condition: 32
8	Conditional	value: 10 condition: 11
9	Operation	operator: 34 operands: 12
10	Operation	operator: 13 operands: 14
11	Operation	operator: 36 operands: 15
12	ExprTuple	16, 43
13	Literal
14	ExprTuple	17, 18
15	ExprTuple	44, 33
16	Operation	operator: 27 operand: 43
17	Operation	operator: 19 operand: 22
18	Operation	operator: 34 operands: 21
19	Literal
20	ExprTuple	22
21	ExprTuple	23, 24
22	Lambda	parameter: 43 body: 26
23	Operation	operator: 27 operand: 44
24	Operation	operator: 29 operand: 33
25	ExprTuple	43
26	Conditional	value: 31 condition: 32
27	Variable
28	ExprTuple	44
29	Literal
30	ExprTuple	33
31	Operation	operator: 34 operands: 35
32	Operation	operator: 36 operands: 37
33	Variable
34	Literal
35	ExprTuple	38, 39
36	Literal
37	ExprTuple	43, 40
38	Operation	operator: 41 operands: 42
39	Literal
40	Variable
41	Literal
42	ExprTuple	43, 44
43	Variable
44	Variable