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 A, Conditional, Lambda, X, c
from proveit.linear_algebra import HilbertSpaces, Hspace, LinMap
from proveit.logic import And, Forall, InClass, InSet
from proveit.physics.quantum import Qmult

# build up the expression from sub-expressions
sub_expr1 = LinMap(Hspace, X)
expr = Lambda([Hspace, X], Conditional(Forall(instance_param_or_params = [A], instance_expr = InSet(Qmult(A, c), sub_expr1), condition = InSet(Qmult(A), sub_expr1)), 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\{\forall_{A~|~\left[A\right] \in \mathcal{L}\left(\mathcal{H}, X\right)}~\left(\left(A \thinspace c\right) \in \mathcal{L}\left(\mathcal{H}, X\right)\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: 28 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operand: 8
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8
6	Literal
7	ExprTuple	9, 10
8	Lambda	parameter: 30 body: 11
9	Operation	operator: 13 operands: 12
10	Operation	operator: 13 operands: 14
11	Conditional	value: 15 condition: 16
12	ExprTuple	31, 17
13	Literal
14	ExprTuple	32, 17
15	Operation	operator: 19 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	21, 23
19	Literal
20	ExprTuple	22, 23
21	Operation	operator: 25 operands: 24
22	Operation	operator: 25 operand: 30
23	Operation	operator: 27 operands: 28
24	ExprTuple	30, 29
25	Literal
26	ExprTuple	30
27	Literal
28	ExprTuple	31, 32
29	Variable
30	Variable
31	Variable
32	Variable