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, Function, Lambda, 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 = ExprTuple(Lambda(var_ket_u, 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(\lvert u \rangle \mapsto \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..\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: 32 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11
9	Lambda	parameter: 25 body: 13
10	Operation	operator: 14 operands: 15
11	Operation	operator: 16 operands: 17
12	ExprTuple	25
13	Operation	operator: 18 operands: 19
14	Literal
15	ExprTuple	32, 20
16	Literal
17	ExprTuple	21, 22
18	Variable
19	ExprTuple	36, 23, 24, 32, 25
20	Operation	operator: 26 operands: 27
21	Operation	operator: 28 operand: 32
22	Literal
23	Variable
24	Variable
25	Variable
26	Literal
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	32
30	Literal
31	Operation	operator: 33 operands: 34
32	Variable
33	Literal
34	ExprTuple	35, 36
35	Literal
36	Variable