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

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([K, H], Equals(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(\left(K, H\right) \mapsto \left(\left(H \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(K\right)\right) = \left(\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)\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	parameters: 2 body: 3
2	ExprTuple	28, 19
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 15 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	19, 11
9	Literal
10	ExprTuple	12, 13
11	Operation	operator: 14 operand: 28
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operand: 21
14	Literal
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21
19	Variable
20	Operation	operator: 22 operand: 28
21	Lambda	parameters: 30 body: 24
22	Literal
23	ExprTuple	28
24	Operation	operator: 25 operands: 26
25	Literal
26	ExprTuple	27, 28
27	Operation	operator: 29 operands: 30
28	Variable
29	Literal
30	ExprTuple	31, 32
31	Variable
32	Variable