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, t
from proveit.linear_algebra import ScalarMult, TensorProd
from proveit.logic import InSet
from proveit.numbers import Interval, one, subtract, zero
from proveit.physics.quantum import NumKet, ket1
from proveit.physics.quantum.QPE import two_pow_t

# build up the expression from sub-expressions
expr = Lambda(k, Conditional(ScalarMult(Function(Variable("_a", latex_format = r"{_{-}a}"), [k]), TensorProd(ket1, 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\{{_{-}a}\left(k\right) \cdot \left(\lvert 1 \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: 26 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	26, 10
8	Operation	operator: 11 operand: 26
9	Operation	operator: 13 operands: 14
10	Operation	operator: 15 operands: 16
11	Variable
12	ExprTuple	26
13	Literal
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19, 20
17	Operation	operator: 21 operand: 35
18	Operation	operator: 22 operands: 23
19	Literal
20	Operation	operator: 24 operands: 25
21	Literal
22	Literal
23	ExprTuple	26, 34
24	Literal
25	ExprTuple	27, 28
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	Variable
35	Literal