Expression of type Lambda

from the theory of proveit.numbers.negation

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 Add, Complex, Neg, subtract

# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(Equals(Neg(subtract(a, b)), Add(Neg(a), b)), 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(-\left(a - b\right)\right) = \left(-a + b\right) \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	25, 28
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: 26 operand: 18
10	Operation	operator: 21 operands: 14
11	Operation	operator: 16 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprTuple	18
14	ExprTuple	19, 28
15	ExprTuple	25, 20
16	Literal
17	ExprTuple	28, 20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 26 operand: 25
20	Literal
21	Literal
22	ExprTuple	25, 24
23	ExprTuple	25
24	Operation	operator: 26 operand: 28
25	Variable
26	Literal
27	ExprTuple	28
28	Variable