Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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())

\left(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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 28 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	28, 11
9	Operation	operator: 12 operand: 28
10	Operation	operator: 31 operands: 13
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	37, 16
14	Literal
15	ExprTuple	37, 17
16	Operation	operator: 35 operand: 20
17	Operation	operator: 31 operands: 19
18	ExprTuple	20
19	ExprTuple	21, 22
20	Operation	operator: 23 operand: 28
21	Operation	operator: 25 operands: 26
22	Operation	operator: 35 operand: 30
23	Literal
24	ExprTuple	28
25	Literal
26	ExprTuple	30, 29
27	ExprTuple	30
28	Variable
29	Operation	operator: 31 operands: 32
30	Literal
31	Literal
32	ExprTuple	33, 34
33	Literal
34	Operation	operator: 35 operand: 37
35	Literal
36	ExprTuple	37
37	Literal