Expression of type Lambda

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, Lambda, 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 = Lambda([a, b], 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(a, b\right) \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 22 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 21 operands: 4
3	Operation	operator: 14 operands: 5
4	ExprTuple	23, 6
5	ExprTuple	7, 8, 9
6	Operation	operator: 10 operands: 22
7	Operation	operator: 12 operands: 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 14 operands: 15
10	Literal
11	ExprTuple	24, 16
12	Literal
13	ExprTuple	25, 16
14	Literal
15	ExprTuple	17, 18
16	Literal
17	Operation	operator: 19 operands: 20
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	24, 25
23	Literal
24	Variable
25	Variable