Expression of type Conditional

from the theory of proveit.numbers.logarithms

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, a, b
from proveit.logic import And, InSet
from proveit.numbers import Less, LessEq, Log, RealPos, greater_eq, one

# build up the expression from sub-expressions
expr = Conditional(greater_eq(Log(a, b), one), And(InSet(a, RealPos), InSet(b, RealPos), And(Less(one, a), LessEq(a, b)).with_total_ordering_style()))

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\{\textrm{log}_a\left(b\right) \geq 1 \textrm{ if } a \in \mathbb{R}^+ ,  b \in \mathbb{R}^+ ,  1 < a \leq b\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 20 operands: 3
2	Operation	operator: 13 operands: 4
3	ExprTuple	22, 5
4	ExprTuple	6, 7, 8
5	Operation	operator: 9 operands: 21
6	Operation	operator: 11 operands: 10
7	Operation	operator: 11 operands: 12
8	Operation	operator: 13 operands: 14
9	Literal
10	ExprTuple	23, 15
11	Literal
12	ExprTuple	24, 15
13	Literal
14	ExprTuple	16, 17
15	Literal
16	Operation	operator: 18 operands: 19
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	23, 24
22	Literal
23	Variable
24	Variable