Expression of type LessEq

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.numbers import Add, Exp, Mult, Neg, four, frac, greater_eq, one, subtract, two
from proveit.physics.quantum.QPE import _eps, _n, _t

# build up the expression from sub-expressions
expr = greater_eq(Neg(frac(one, Mult(four, Exp(subtract(Exp(two, subtract(_t, _n)), one), two)))), Neg(frac(one, Mult(four, Exp(Add(one, frac(one, Mult(two, _eps))), two)))))

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(-\frac{1}{4 \cdot \left(2^{t - n} - 1\right)^{2}}\right) \geq \left(-\frac{1}{4 \cdot \left(1 + \frac{1}{2 \cdot \epsilon}\right)^{2}}\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	reversed	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 43 operand: 7
4	Operation	operator: 43 operand: 8
5	ExprTuple	7
6	ExprTuple	8
7	Operation	operator: 27 operands: 9
8	Operation	operator: 27 operands: 10
9	ExprTuple	34, 11
10	ExprTuple	34, 12
11	Operation	operator: 35 operands: 13
12	Operation	operator: 35 operands: 14
13	ExprTuple	16, 15
14	ExprTuple	16, 17
15	Operation	operator: 29 operands: 18
16	Literal
17	Operation	operator: 29 operands: 19
18	ExprTuple	20, 39
19	ExprTuple	21, 39
20	Operation	operator: 37 operands: 22
21	Operation	operator: 37 operands: 23
22	ExprTuple	34, 24
23	ExprTuple	25, 26
24	Operation	operator: 27 operands: 28
25	Operation	operator: 29 operands: 30
26	Operation	operator: 43 operand: 34
27	Literal
28	ExprTuple	34, 32
29	Literal
30	ExprTuple	39, 33
31	ExprTuple	34
32	Operation	operator: 35 operands: 36
33	Operation	operator: 37 operands: 38
34	Literal
35	Literal
36	ExprTuple	39, 40
37	Literal
38	ExprTuple	41, 42
39	Literal
40	Literal
41	Literal
42	Operation	operator: 43 operand: 45
43	Literal
44	ExprTuple	45
45	Literal