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, x
from proveit.logic import Equals, InSet
from proveit.numbers import Abs, Exp, Real, sqrt, two

# build up the expression from sub-expressions
expr = Lambda(x, Conditional(Equals(Abs(x), sqrt(Exp(x, two))), InSet(x, Real)))

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())

x \mapsto \left\{\left|x\right| = \sqrt{(x^{2})} \textrm{ if } x \in \mathbb{R}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 20 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	20, 10
8	Operation	operator: 11 operand: 20
9	Operation	operator: 16 operands: 13
10	Literal
11	Literal
12	ExprTuple	20
13	ExprTuple	14, 15
14	Operation	operator: 16 operands: 17
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	20, 22
18	Literal
19	ExprTuple	21, 22
20	Variable
21	Literal
22	Literal