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, Function, Lambda, Variable, k
from proveit.logic import InSet
from proveit.numbers import Exp, Mult, e, i, pi, two
from proveit.physics.quantum.QPE import _m_domain, _phase

# build up the expression from sub-expressions
expr = Lambda(k, Conditional(Mult(Function(Variable("_a", latex_format = r"{_{-}a}"), [k]), Exp(e, Mult(two, pi, i, _phase, 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\{{_{-}a}\left(k\right) \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 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: 26 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 19 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	26, 9
7	Operation	operator: 10 operand: 26
8	Operation	operator: 29 operands: 12
9	Operation	operator: 13 operands: 14
10	Variable
11	ExprTuple	26
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17, 18
15	Literal
16	Operation	operator: 19 operands: 20
17	Literal
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	33, 23, 24, 25, 26
21	Literal
22	ExprTuple	27, 28
23	Literal
24	Literal
25	Literal
26	Variable
27	Operation	operator: 29 operands: 30
28	Operation	operator: 31 operand: 35
29	Literal
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	35
33	Literal
34	Literal
35	Literal