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, b
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Integer, frac
from proveit.physics.quantum.QPE import _delta_b, _phase, _two_pow_t

# build up the expression from sub-expressions
expr = Lambda(b, Conditional(Equals(_phase, Add(frac(b, _two_pow_t), _delta_b)), InSet(b, Integer)))

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())

b \mapsto \left\{\varphi = \left(\frac{b}{2^{t}} + \delta_{b}\right) \textrm{ if } b \in \mathbb{Z}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 20 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	20, 10
8	Literal
9	Operation	operator: 11 operands: 12
10	Literal
11	Literal
12	ExprTuple	13, 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operand: 20
15	Literal
16	ExprTuple	20, 19
17	Literal
18	ExprTuple	20
19	Operation	operator: 21 operands: 22
20	Variable
21	Literal
22	ExprTuple	23, 24
23	Literal
24	Literal