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, NotEquals
from proveit.numbers import Abs, Complex, frac, zero

# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(Equals(Abs(frac(a, b)), frac(Abs(a), Abs(b))), And(InSet(a, Complex), InSet(b, Complex), NotEquals(b, zero))))

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|\frac{a}{b}\right| = \frac{\left|a\right|}{\left|b\right|} \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{C} ,  b \neq 0\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 26 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, 12
8	Operation	operator: 28 operand: 20
9	Operation	operator: 25 operands: 14
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	Operation	operator: 18 operands: 19
13	ExprTuple	20
14	ExprTuple	21, 22
15	ExprTuple	30, 23
16	Literal
17	ExprTuple	31, 23
18	Literal
19	ExprTuple	31, 24
20	Operation	operator: 25 operands: 26
21	Operation	operator: 28 operand: 30
22	Operation	operator: 28 operand: 31
23	Literal
24	Literal
25	Literal
26	ExprTuple	30, 31
27	ExprTuple	30
28	Literal
29	ExprTuple	31
30	Variable
31	Variable