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, i, m, n
from proveit.core_expr_types import a_i, b_i, lambda_i
from proveit.linear_algebra import ScalarMult
from proveit.logic import InSet
from proveit.numbers import Interval, Min, one
from proveit.physics.quantum import Ket, Qmult

# build up the expression from sub-expressions
expr = Lambda(i, Conditional(ScalarMult(lambda_i, Qmult(Ket(a_i), Ket(b_i))), InSet(i, Interval(one, Min(m, n)))))

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())

i \mapsto \left\{\lambda_{i} \cdot \left(\lvert a_{i} \rangle \thinspace \lvert b_{i} \rangle\right) \textrm{ if } i \in \{1~\ldotp \ldotp~{\rm Min}\left(m, n\right)\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 32 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	32, 10
8	IndexedVar	variable: 11 index: 32
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operands: 15
11	Variable
12	Literal
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	18, 19
16	Operation	operator: 21 operand: 25
17	Operation	operator: 21 operand: 26
18	Literal
19	Operation	operator: 23 operands: 24
20	ExprTuple	25
21	Literal
22	ExprTuple	26
23	Literal
24	ExprTuple	27, 28
25	IndexedVar	variable: 29 index: 32
26	IndexedVar	variable: 30 index: 32
27	Variable
28	Variable
29	Variable
30	Variable
31	ExprTuple	32
32	Variable