Expression of type Conditional

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, Function, U, Variable, s, t
from proveit.logic import And, Forall, InSet
from proveit.physics.quantum import normalized_var_ket_u, var_ket_u
from proveit.physics.quantum.QPE import phase, s_ket_domain

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [phase], instance_expr = Function(Variable("_b", latex_format = r"{_{-}b}"), [s, t, U, var_ket_u, phase])), And(InSet(var_ket_u, s_ket_domain), normalized_var_ket_u))

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\{\forall_{\varphi}~{_{-}b}\left(s, t, U, \lvert u \rangle, \varphi\right) \textrm{ if } \lvert u \rangle \in \mathbb{C}^{2^{s}} ,  \left \|\lvert u \rangle\right \| = 1\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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