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, e
from proveit.logic import InSet
from proveit.numbers import Add, Exp, LessEq, Mult, four, frac, one, two
from proveit.physics.quantum.QPE import Pfail, _e_domain

# build up the expression from sub-expressions
expr = Lambda(e, Conditional(LessEq(Pfail(e), Add(frac(one, Mult(two, e)), frac(one, Mult(four, Exp(e, two))))), InSet(e, _e_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())

e \mapsto \left\{\left[P_{\rm fail}\right]\left(e\right) \leq \left(\frac{1}{2 \cdot e} + \frac{1}{4 \cdot e^{2}}\right) \textrm{ if } e \in \{1~\ldotp \ldotp~2^{t - 1} - 2\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 39 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	39, 10
8	Operation	operator: 11 operand: 39
9	Operation	operator: 37 operands: 13
10	Operation	operator: 14 operands: 15
11	Literal
12	ExprTuple	39
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	45, 18
16	Operation	operator: 20 operands: 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 37 operands: 22
19	ExprTuple	45, 23
20	Literal
21	ExprTuple	45, 24
22	ExprTuple	25, 26
23	Operation	operator: 28 operands: 27
24	Operation	operator: 28 operands: 29
25	Operation	operator: 35 operands: 30
26	Operation	operator: 43 operand: 40
27	ExprTuple	40, 39
28	Literal
29	ExprTuple	32, 33
30	ExprTuple	40, 34
31	ExprTuple	40
32	Literal
33	Operation	operator: 35 operands: 36
34	Operation	operator: 37 operands: 38
35	Literal
36	ExprTuple	39, 40
37	Literal
38	ExprTuple	41, 42
39	Variable
40	Literal
41	Literal
42	Operation	operator: 43 operand: 45
43	Literal
44	ExprTuple	45
45	Literal