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, H, K, x, y
from proveit.linear_algebra import InnerProd, InnerProdSpaces, VecSpaces
from proveit.logic import And, Forall, InClass, InSet

# build up the expression from sub-expressions
expr = ExprTuple(InClass(H, InnerProdSpaces(K)), And(InClass(H, VecSpaces(K)), Forall(instance_param_or_params = [x, y], instance_expr = InSet(InnerProd(x, y), K))))

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(H \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(K\right), \left(H \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right) \land \left[\forall_{x, y}~\left(\left \langle x, y\right \rangle \in K\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: 10 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	14, 6
4	Literal
5	ExprTuple	7, 8
6	Operation	operator: 9 operand: 23
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operand: 16
9	Literal
10	Literal
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16
14	Variable
15	Operation	operator: 17 operand: 23
16	Lambda	parameters: 25 body: 19
17	Literal
18	ExprTuple	23
19	Operation	operator: 20 operands: 21
20	Literal
21	ExprTuple	22, 23
22	Operation	operator: 24 operands: 25
23	Variable
24	Literal
25	ExprTuple	26, 27
26	Variable
27	Variable