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, VecSpaces
from proveit.logic import Forall, InClass, InSet

# build up the expression from sub-expressions
expr = ExprTuple(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{VecSpaces}\left(K\right), \forall_{x, y}~\left(\left \langle x, y\right \rangle \in K\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: 3 operands: 4
2	Operation	operator: 5 operand: 9
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9
7	Variable
8	Operation	operator: 10 operand: 16
9	Lambda	parameters: 18 body: 12
10	Literal
11	ExprTuple	16
12	Operation	operator: 13 operands: 14
13	Literal
14	ExprTuple	15, 16
15	Operation	operator: 17 operands: 18
16	Variable
17	Literal
18	ExprTuple	19, 20
19	Variable
20	Variable