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, a, b
from proveit.logic import And, Equals, InSet
from proveit.numbers import Abs, Complex, subtract

# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(Equals(Abs(subtract(a, b)), Abs(subtract(b, a))), 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| = \left|b - a\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	31, 30
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 operand: 19
10	Operation	operator: 14 operand: 20
11	Operation	operator: 17 operands: 16
12	Operation	operator: 17 operands: 18
13	ExprTuple	19
14	Literal
15	ExprTuple	20
16	ExprTuple	31, 21
17	Literal
18	ExprTuple	30, 21
19	Operation	operator: 23 operands: 22
20	Operation	operator: 23 operands: 24
21	Literal
22	ExprTuple	31, 25
23	Literal
24	ExprTuple	30, 26
25	Operation	operator: 28 operand: 30
26	Operation	operator: 28 operand: 31
27	ExprTuple	30
28	Literal
29	ExprTuple	31
30	Variable
31	Variable