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 Real
from proveit.physics.quantum.QPE import Pfail, _e_domain

# build up the expression from sub-expressions
expr = Lambda(e, Conditional(InSet(Pfail(e), Real), 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) \in \mathbb{R} \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: 14 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 5 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	14, 9
7	Operation	operator: 10 operand: 14
8	Literal
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	14
12	Literal
13	ExprTuple	30, 15
14	Variable
15	Operation	operator: 24 operands: 16
16	ExprTuple	17, 18
17	Operation	operator: 19 operands: 20
18	Operation	operator: 28 operand: 23
19	Literal
20	ExprTuple	23, 22
21	ExprTuple	23
22	Operation	operator: 24 operands: 25
23	Literal
24	Literal
25	ExprTuple	26, 27
26	Literal
27	Operation	operator: 28 operand: 30
28	Literal
29	ExprTuple	30
30	Literal