Expression of type Lambda

from the theory of proveit.numbers.number_sets.complex_numbers

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 Lambda, a, b
from proveit.logic import Equals
from proveit.numbers import Add, Conjugate, Mult, i, subtract

# build up the expression from sub-expressions
sub_expr1 = Mult(i, b)
expr = Lambda([a, b], Equals(Conjugate(Add(a, sub_expr1)), subtract(a, sub_expr1)))

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 + \left(\mathsf{i} \cdot b\right)\right)^*\right) = \left(a - \left(\mathsf{i} \cdot b\right)\right)\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	16, 21
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 12 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	16, 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 14 operand: 17
12	Literal
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	17
16	Variable
17	Operation	operator: 18 operands: 19
18	Literal
19	ExprTuple	20, 21
20	Literal
21	Variable