Expression of type Lambda

from the theory of proveit.numbers.exponentiation

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, x
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Exp, Log, RealPos, one

# build up the expression from sub-expressions
expr = Lambda([a, x], Conditional(Equals(Exp(a, Log(a, x)), x), And(InSet(a, RealPos), InSet(x, RealPos), NotEquals(a, one))))

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, x\right) \mapsto \left\{a^{\textrm{log}_a\left(x\right)} = x \textrm{ if } a \in \mathbb{R}^+ ,  x \in \mathbb{R}^+ ,  a \neq 1\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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