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
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Exp, Interval, Mult, e, i, one, pi, two, zero
from proveit.physics.quantum import Ket
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
sub_expr1 = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), Ket(k))
expr = Lambda(k, Equals(Conditional(sub_expr1, InSet(k, Interval(Add(zero, one), one))), Conditional(sub_expr1, InSet(k, Interval(one, one)))))

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(\left\{\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle \textrm{ if } k \in \{0 + 1~\ldotp \ldotp~1\}\right.. = \left\{\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle \textrm{ if } k \in \{1~\ldotp \ldotp~1\}\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: 38 body: 1
1	Operation	operator: 2 operands: 3
2	Literal
3	ExprTuple	4, 5
4	Conditional	value: 7 condition: 6
5	Conditional	value: 7 condition: 8
6	Operation	operator: 12 operands: 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operands: 13
9	ExprTuple	38, 14
10	Literal
11	ExprTuple	15, 16
12	Literal
13	ExprTuple	38, 17
14	Operation	operator: 23 operands: 18
15	Operation	operator: 19 operands: 20
16	Operation	operator: 21 operand: 38
17	Operation	operator: 23 operands: 24
18	ExprTuple	25, 33
19	Literal
20	ExprTuple	26, 27
21	Literal
22	ExprTuple	38
23	Literal
24	ExprTuple	33, 33
25	Operation	operator: 28 operands: 29
26	Literal
27	Operation	operator: 30 operands: 31
28	Literal
29	ExprTuple	32, 33
30	Literal
31	ExprTuple	34, 35, 36, 37, 38
32	Literal
33	Literal
34	Literal
35	Literal
36	Literal
37	Literal
38	Variable