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, a, b
from proveit.logic import And, InSet
from proveit.numbers import Abs, Exp, LessEq, Real, two

# build up the expression from sub-expressions
sub_expr1 = Abs(a)
expr = Lambda([a, b], Conditional(LessEq(Exp(sub_expr1, two), Exp(b, two)), And(InSet(a, Real), InSet(b, Real), LessEq(sub_expr1, b))))

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\right|^{2} \leq b^{2} \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{R} ,  \left|a\right| \leq b\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	27, 24
2	Conditional	value: 3 condition: 4
3	Operation	operator: 19 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11, 12
8	Operation	operator: 14 operands: 13
9	Operation	operator: 14 operands: 15
10	Operation	operator: 17 operands: 16
11	Operation	operator: 17 operands: 18
12	Operation	operator: 19 operands: 20
13	ExprTuple	23, 21
14	Literal
15	ExprTuple	24, 21
16	ExprTuple	27, 22
17	Literal
18	ExprTuple	24, 22
19	Literal
20	ExprTuple	23, 24
21	Literal
22	Literal
23	Operation	operator: 25 operand: 27
24	Variable
25	Literal
26	ExprTuple	27
27	Variable