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, B, Composition, Conditional, Lambda, X, Y
from proveit.linear_algebra import Hspace, LinMap
from proveit.logic import And, Equals, InSet
from proveit.physics.quantum import Qmult

# build up the expression from sub-expressions
sub_expr1 = Qmult(A)
sub_expr2 = Qmult(B)
expr = Lambda([A, B], Conditional(Equals(Qmult(A, B), Composition(sub_expr1, sub_expr2)), And(InSet(sub_expr1, LinMap(X, Y)), InSet(sub_expr2, LinMap(Hspace, X)))))

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(A, B\right) \mapsto \left\{\left(A \thinspace B\right) = \left(\left[A\right] \circ \left[B\right]\right) \textrm{ if } \left[A\right] \in \mathcal{L}\left(X, Y\right) ,  \left[B\right] \in \mathcal{L}\left(\mathcal{H}, X\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: 12 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	Operation	operator: 24 operands: 12
9	Operation	operator: 13 operands: 14
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	ExprTuple	28, 30
13	Literal
14	ExprTuple	18, 20
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21
18	Operation	operator: 24 operand: 28
19	Operation	operator: 26 operands: 23
20	Operation	operator: 24 operand: 30
21	Operation	operator: 26 operands: 27
22	ExprTuple	28
23	ExprTuple	32, 29
24	Literal
25	ExprTuple	30
26	Literal
27	ExprTuple	31, 32
28	Variable
29	Variable
30	Variable
31	Variable
32	Variable