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 Conditional, Lambda, k, m
from proveit.logic import InSet
from proveit.numbers import Exp, Mult, e, frac, i, pi, subtract, two
from proveit.physics.quantum.QPE import _m_domain, _phase, _two_pow_t

# build up the expression from sub-expressions
expr = Lambda(k, Conditional(Exp(Exp(e, Mult(two, pi, i, subtract(_phase, frac(m, _two_pow_t)))), k), InSet(k, _m_domain)))

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())

k \mapsto \left\{(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\varphi - \frac{m}{2^{t}}\right)})^{k} \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 9 body: 2
1	ExprTuple	9
2	Conditional	value: 3 condition: 4
3	Operation	operator: 38 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 38 operands: 11
9	Variable
10	Operation	operator: 12 operands: 13
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16, 17
14	Literal
15	Operation	operator: 18 operands: 19
16	Literal
17	Operation	operator: 25 operands: 20
18	Literal
19	ExprTuple	40, 21, 22, 23
20	ExprTuple	37, 24
21	Literal
22	Literal
23	Operation	operator: 25 operands: 26
24	Operation	operator: 31 operand: 30
25	Literal
26	ExprTuple	28, 29
27	ExprTuple	30
28	Literal
29	Operation	operator: 31 operand: 33
30	Literal
31	Literal
32	ExprTuple	33
33	Operation	operator: 34 operands: 35
34	Literal
35	ExprTuple	36, 37
36	Variable
37	Operation	operator: 38 operands: 39
38	Literal
39	ExprTuple	40, 41
40	Literal
41	Literal