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, l
from proveit.logic import InSet
from proveit.numbers import Exp, frac, one, subtract, two
from proveit.physics.quantum.QPE import _pos_domain

# build up the expression from sub-expressions
expr = Lambda(l, Conditional(frac(one, Exp(subtract(l, one), two)), InSet(l, _pos_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())

l \mapsto \left\{\frac{1}{\left(l - 1\right)^{2}} \textrm{ if } l \in \{e + 1~\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: 21 body: 2
1	ExprTuple	21
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	31, 9
7	Literal
8	ExprTuple	21, 10
9	Operation	operator: 19 operands: 11
10	Operation	operator: 12 operands: 13
11	ExprTuple	14, 23
12	Literal
13	ExprTuple	15, 16
14	Operation	operator: 25 operands: 17
15	Operation	operator: 25 operands: 18
16	Operation	operator: 19 operands: 20
17	ExprTuple	21, 28
18	ExprTuple	22, 31
19	Literal
20	ExprTuple	23, 24
21	Variable
22	Variable
23	Literal
24	Operation	operator: 25 operands: 26
25	Literal
26	ExprTuple	27, 28
27	Literal
28	Operation	operator: 29 operand: 31
29	Literal
30	ExprTuple	31
31	Literal