Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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(\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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	23, 32
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13
10	Operation	operator: 15 operand: 20
11	Operation	operator: 15 operand: 23
12	Operation	operator: 18 operands: 17
13	Operation	operator: 18 operands: 19
14	ExprTuple	20
15	Literal
16	ExprTuple	23
17	ExprTuple	23, 21
18	Literal
19	ExprTuple	32, 21
20	Operation	operator: 29 operands: 22
21	Literal
22	ExprTuple	23, 24
23	Variable
24	Operation	operator: 25 operands: 26
25	Literal
26	ExprTuple	27, 28
27	Literal
28	Operation	operator: 29 operands: 30
29	Literal
30	ExprTuple	31, 32
31	Literal
32	Variable