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, m
from proveit.logic import Equals, InSet
from proveit.physics.quantum import NumBra, Qmult
from proveit.physics.quantum.QPE import _Psi_ket, _alpha_m, _m_domain, _t

# build up the expression from sub-expressions
expr = Lambda(m, Conditional(Equals(_alpha_m, Qmult(NumBra(m, _t), _Psi_ket)), InSet(m, _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())

m \mapsto \left\{\alpha_{m} = \left({_{t}}\langle m \rvert \thinspace \lvert \Psi \rangle\right) \textrm{ if } m \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: 25 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	25, 10
8	Operation	operator: 11 operand: 25
9	Operation	operator: 13 operands: 14
10	Operation	operator: 15 operands: 16
11	Literal
12	ExprTuple	25
13	Literal
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19, 20
17	Operation	operator: 21 operands: 22
18	Literal
19	Literal
20	Operation	operator: 23 operands: 24
21	Literal
22	ExprTuple	25, 33
23	Literal
24	ExprTuple	26, 27
25	Variable
26	Operation	operator: 28 operands: 29
27	Operation	operator: 30 operand: 34
28	Literal
29	ExprTuple	32, 33
30	Literal
31	ExprTuple	34
32	Literal
33	Literal
34	Literal