Expression of type Lambda

from the theory of proveit.numbers.exponentiation

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 And, Equals, InSet
from proveit.numbers import Mult, Real, greater_eq, sqrt, zero

# build up the expression from sub-expressions
sub_expr1 = sqrt(x)
expr = Lambda(x, Conditional(Equals(Mult(sub_expr1, sub_expr1), x), And(InSet(x, Real), greater_eq(x, 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())

x \mapsto \left\{\left(\sqrt{x} \cdot \sqrt{x}\right) = x \textrm{ if } x \in \mathbb{R} ,  x \geq 0\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 23 body: 2
1	ExprTuple	23
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 23
7	Literal
8	ExprTuple	10, 11
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operands: 15
11	Operation	operator: 16 operands: 17
12	Literal
13	ExprTuple	18, 18
14	Literal
15	ExprTuple	23, 19
16	Literal
17	ExprTuple	20, 23
18	Operation	operator: 21 operands: 22
19	Literal
20	Literal
21	Literal
22	ExprTuple	23, 24
23	Variable
24	Operation	operator: 25 operands: 26
25	Literal
26	ExprTuple	27, 28
27	Literal
28	Literal