Expression of type Lambda

from the theory of proveit.physics.quantum.algebra

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 Conditional, Lambda, X, x
from proveit.linear_algebra import HilbertSpaces, Hspace, LinMap
from proveit.logic import And, InClass, InSet

# build up the expression from sub-expressions
expr = Lambda([Hspace, X], Conditional(InSet(x, LinMap(Hspace, X)), And(InClass(Hspace, HilbertSpaces), InClass(X, HilbertSpaces))))

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(\mathcal{H}, X\right) \mapsto \left\{x \in \mathcal{L}\left(\mathcal{H}, X\right) \textrm{ if } \mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces} ,  X \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 13 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11
8	Variable
9	Operation	operator: 12 operands: 13
10	Operation	operator: 15 operands: 14
11	Operation	operator: 15 operands: 16
12	Literal
13	ExprTuple	17, 18
14	ExprTuple	17, 19
15	Literal
16	ExprTuple	18, 19
17	Variable
18	Variable
19	Literal