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, t
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Interval, one, subtract, zero
from proveit.physics.quantum import NumKet, ket0
from proveit.physics.quantum.QPE import two_pow_t

# build up the expression from sub-expressions
expr = Lambda(k, Conditional(Equals(NumKet(k, Add(t, one)), TensorProd(ket0, NumKet(k, t))), InSet(k, Interval(zero, subtract(two_pow_t, 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\{\lvert k \rangle_{t + 1} = \left(\lvert 0 \rangle {\otimes} \lvert k \rangle_{t}\right) \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: 29 body: 2
1	ExprTuple	29
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	29, 11
9	Operation	operator: 24 operands: 12
10	Operation	operator: 13 operands: 14
11	Operation	operator: 15 operands: 16
12	ExprTuple	29, 17
13	Literal
14	ExprTuple	18, 19
15	Literal
16	ExprTuple	28, 20
17	Operation	operator: 26 operands: 21
18	Operation	operator: 22 operand: 28
19	Operation	operator: 24 operands: 25
20	Operation	operator: 26 operands: 27
21	ExprTuple	37, 38
22	Literal
23	ExprTuple	28
24	Literal
25	ExprTuple	29, 37
26	Literal
27	ExprTuple	30, 31
28	Literal
29	Variable
30	Operation	operator: 32 operands: 33
31	Operation	operator: 34 operand: 38
32	Literal
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	38
36	Literal
37	Variable
38	Literal