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 Equals, InSet
from proveit.numbers import one, subtract
from proveit.physics.quantum.QPE import Pfail, Psuccess, _e_domain

# build up the expression from sub-expressions
expr = Lambda(e, Conditional(Equals(Psuccess(e), subtract(one, Pfail(e))), 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 success}\right]\left(e\right) = \left(1 - \left[P_{\rm fail}\right]\left(e\right)\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: 27 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	27, 10
8	Operation	operator: 11 operand: 27
9	Operation	operator: 30 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	36, 15
13	Literal
14	ExprTuple	36, 16
15	Operation	operator: 34 operand: 19
16	Operation	operator: 30 operands: 18
17	ExprTuple	19
18	ExprTuple	20, 21
19	Operation	operator: 22 operand: 27
20	Operation	operator: 24 operands: 25
21	Operation	operator: 34 operand: 29
22	Literal
23	ExprTuple	27
24	Literal
25	ExprTuple	29, 28
26	ExprTuple	29
27	Variable
28	Operation	operator: 30 operands: 31
29	Literal
30	Literal
31	ExprTuple	32, 33
32	Literal
33	Operation	operator: 34 operand: 36
34	Literal
35	ExprTuple	36
36	Literal