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, x, y
from proveit.logic import And, Equals, InSet
from proveit.numbers import Abs, Complex

# build up the expression from sub-expressions
expr = Lambda([x, y], Conditional(Equals(Abs(x), Abs(y)), And(InSet(x, Complex), InSet(y, Complex), Equals(x, y))))

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(x, y\right) \mapsto \left\{\left|x\right| = \left|y\right| \textrm{ if } x \in \mathbb{C} ,  y \in \mathbb{C} ,  x = y\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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