Expression of type Lambda

from the theory of proveit.physics.quantum.QPE

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 Lambda, Variable
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.numbers import Exp, Mult, Neg, e, frac, i, one, pi, sqrt, two
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(sub_expr1, ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1))))

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())

{_{-}a} \mapsto \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-{_{-}a}} \cdot \varphi} \cdot \lvert 1 \rangle\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	parameter: 39 body: 1
1	Operation	operator: 13 operands: 2
2	ExprTuple	3, 4
3	Operation	operator: 19 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	26, 8
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 33 operands: 11
9	Operation	operator: 22 operand: 16
10	Operation	operator: 13 operands: 14
11	ExprTuple	35, 15
12	ExprTuple	16
13	Literal
14	ExprTuple	17, 18
15	Operation	operator: 19 operands: 20
16	Literal
17	Operation	operator: 33 operands: 21
18	Operation	operator: 22 operand: 26
19	Literal
20	ExprTuple	26, 35
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26
24	Literal
25	Operation	operator: 27 operands: 28
26	Literal
27	Literal
28	ExprTuple	35, 29, 30, 31, 32
29	Literal
30	Literal
31	Operation	operator: 33 operands: 34
32	Literal
33	Literal
34	ExprTuple	35, 36
35	Literal
36	Operation	operator: 37 operand: 39
37	Literal
38	ExprTuple	39
39	Variable