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, b
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Exp, subtract, two

# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(Equals(Exp(subtract(a, b), two), Exp(subtract(b, a), two)), And(InSet(a, Complex), InSet(b, 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(a, b\right) \mapsto \left\{\left(a - b\right)^{2} = \left(b - a\right)^{2} \textrm{ if } a \in \mathbb{C} ,  b \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: 1 body: 2
1	ExprTuple	32, 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 operands: 13
10	Operation	operator: 14 operands: 15
11	Operation	operator: 17 operands: 16
12	Operation	operator: 17 operands: 18
13	ExprTuple	19, 21
14	Literal
15	ExprTuple	20, 21
16	ExprTuple	32, 22
17	Literal
18	ExprTuple	31, 22
19	Operation	operator: 24 operands: 23
20	Operation	operator: 24 operands: 25
21	Literal
22	Literal
23	ExprTuple	32, 26
24	Literal
25	ExprTuple	31, 27
26	Operation	operator: 29 operand: 31
27	Operation	operator: 29 operand: 32
28	ExprTuple	31
29	Literal
30	ExprTuple	32
31	Variable
32	Variable