Expression of type Lambda

from the theory of proveit.numbers.multiplication

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 Complex, Mult, Neg

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

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

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 13 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, 9
6	Literal
7	ExprTuple	10, 11
8	Operation	operator: 23 operand: 17
9	Operation	operator: 19 operands: 13
10	Operation	operator: 15 operands: 14
11	Operation	operator: 15 operands: 16
12	ExprTuple	17
13	ExprTuple	25, 22
14	ExprTuple	25, 18
15	Literal
16	ExprTuple	22, 18
17	Operation	operator: 19 operands: 20
18	Literal
19	Literal
20	ExprTuple	21, 22
21	Operation	operator: 23 operand: 25
22	Variable
23	Literal
24	ExprTuple	25
25	Variable