Expression of type Lambda

from the theory of proveit.numbers.absolute_value

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, r, theta
from proveit.logic import And, Equals, InSet
from proveit.numbers import Abs, Exp, Mult, Real, e, i

# build up the expression from sub-expressions
expr = Lambda([r, theta], Conditional(Equals(Abs(Mult(r, Exp(e, Mult(i, theta)))), Abs(r)), And(InSet(r, Real), InSet(theta, Real))))

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(r, \theta\right) \mapsto \left\{\left|r \cdot \mathsf{e}^{\mathsf{i} \cdot \theta}\right| = \left|r\right| \textrm{ if } r \in \mathbb{R} ,  \theta \in \mathbb{R}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	22, 31
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 14 operand: 19
10	Operation	operator: 14 operand: 22
11	Operation	operator: 17 operands: 16
12	Operation	operator: 17 operands: 18
13	ExprTuple	19
14	Literal
15	ExprTuple	22
16	ExprTuple	22, 20
17	Literal
18	ExprTuple	31, 20
19	Operation	operator: 28 operands: 21
20	Literal
21	ExprTuple	22, 23
22	Variable
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