Expression of type And

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 eps, n, t
from proveit.logic import And, InSet
from proveit.numbers import Add, Ceil, Log, Mult, NaturalPos, frac, greater_eq, one, two

# build up the expression from sub-expressions
expr = And(InSet(t, NaturalPos), greater_eq(t, Add(n, Ceil(Log(two, Add(two, frac(one, Mult(two, eps))))))))

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(t \in \mathbb{N}^+\right) \land \left(t \geq \left(n + \left\lceil \textrm{log}_2\left(2 + \frac{1}{2 \cdot \epsilon}\right)\right\rceil\right)\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',)

# 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: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	11, 9
7	Literal
8	ExprTuple	10, 11
9	Literal
10	Operation	operator: 21 operands: 12
11	Variable
12	ExprTuple	13, 14
13	Variable
14	Operation	operator: 15 operand: 17
15	Literal
16	ExprTuple	17
17	Operation	operator: 18 operands: 19
18	Literal
19	ExprTuple	30, 20
20	Operation	operator: 21 operands: 22
21	Literal
22	ExprTuple	30, 23
23	Operation	operator: 24 operands: 25
24	Literal
25	ExprTuple	26, 27
26	Literal
27	Operation	operator: 28 operands: 29
28	Literal
29	ExprTuple	30, 31
30	Literal
31	Variable