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, l
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Exp, Mult, four, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain

# build up the expression from sub-expressions
sub_expr1 = Exp(_diff_l_scaled_delta_floor, two)
sub_expr2 = frac(one, Mult(four, sub_expr1))
sub_expr3 = Mult(frac(one, four), frac(one, sub_expr1))
sub_expr4 = InSet(l, _neg_domain)
expr = ExprTuple(Forall(instance_param_or_params = [l], instance_expr = Equals(sub_expr2, sub_expr3), domain = _neg_domain), Equals(Lambda(l, Conditional(sub_expr2, sub_expr4)), Lambda(l, Conditional(sub_expr3, sub_expr4))).with_wrapping_at(2))

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_{l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}}~\left(\frac{1}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} = \left(\frac{1}{4} \cdot \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right)\right), \begin{array}{c} \begin{array}{l} \left[l \mapsto \left\{\frac{1}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}\right..\right] =  \\ \left[l \mapsto \left\{\frac{1}{4} \cdot \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}\right..\right] \end{array} \end{array}\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 15 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameter: 49 body: 9
7	Lambda	parameter: 49 body: 10
8	Lambda	parameter: 49 body: 12
9	Conditional	value: 13 condition: 14
10	Conditional	value: 19 condition: 14
11	ExprTuple	49
12	Conditional	value: 20 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	49, 21
19	Operation	operator: 33 operands: 22
20	Operation	operator: 57 operands: 23
21	Operation	operator: 24 operands: 25
22	ExprTuple	63, 26
23	ExprTuple	27, 28
24	Literal
25	ExprTuple	29, 30
26	Operation	operator: 57 operands: 31
27	Operation	operator: 33 operands: 32
28	Operation	operator: 33 operands: 34
29	Operation	operator: 53 operands: 35
30	Operation	operator: 59 operand: 40
31	ExprTuple	37, 38
32	ExprTuple	63, 37
33	Literal
34	ExprTuple	63, 38
35	ExprTuple	39, 63
36	ExprTuple	40
37	Literal
38	Operation	operator: 64 operands: 41
39	Operation	operator: 59 operand: 45
40	Operation	operator: 53 operands: 43
41	ExprTuple	44, 68
42	ExprTuple	45
43	ExprTuple	46, 63
44	Operation	operator: 53 operands: 47
45	Operation	operator: 64 operands: 48
46	Variable
47	ExprTuple	49, 50
48	ExprTuple	68, 51
49	Variable
50	Operation	operator: 59 operand: 55
51	Operation	operator: 53 operands: 54
52	ExprTuple	55
53	Literal
54	ExprTuple	69, 56
55	Operation	operator: 57 operands: 58
56	Operation	operator: 59 operand: 63
57	Literal
58	ExprTuple	61, 62
59	Literal
60	ExprTuple	63
61	Operation	operator: 64 operands: 65
62	Operation	operator: 66 operand: 70
63	Literal
64	Literal
65	ExprTuple	68, 69
66	Literal
67	ExprTuple	70
68	Literal
69	Literal
70	Literal