Expression of type Lambda

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 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 = 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(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)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	27, 18
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 14 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	18, 10
8	Literal
9	ExprTuple	11, 12
10	Operation	operator: 13 operand: 27
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operand: 20
13	Literal
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20
18	Variable
19	Operation	operator: 21 operand: 27
20	Lambda	parameters: 29 body: 23
21	Literal
22	ExprTuple	27
23	Operation	operator: 24 operands: 25
24	Literal
25	ExprTuple	26, 27
26	Operation	operator: 28 operands: 29
27	Variable
28	Literal
29	ExprTuple	30, 31
30	Variable
31	Variable