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, ConditionalSet, Lambda, Variable, t
from proveit.logic import Equals, NotEquals, Set
from proveit.numbers import Add, one
from proveit.physics.quantum import CONTROL, I
from proveit.physics.quantum.circuits import Gate, MultiQubitElem

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(Variable("_b", latex_format = r"{_{-}b}"), t)
expr = Lambda(sub_expr1, ConditionalSet(Conditional(MultiQubitElem(element = CONTROL, targets = Set(Add(t, one))), Equals(sub_expr2, sub_expr1)), Conditional(Gate(operation = I).with_implicit_representation(), NotEquals(sub_expr2, sub_expr1))))

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())

{_{-}a} \mapsto \left\{\begin{array}{ccc}\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{CONTROL~\mbox{on}~\left\{t + 1\right\}} & \qw 
} \end{array} \textrm{ if } \left({_{-}b} + t\right) = {_{-}a} \\ \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array} \textrm{ if } \left({_{-}b} + t\right) \neq {_{-}a}\end{array}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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