Expression of type Lambda

from the theory of proveit.numbers.numerals.binaries

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, b
from proveit.logic import And, InSet
from proveit.numbers import Bit, LessEq, Natural, one, zero

# build up the expression from sub-expressions
expr = Lambda(b, Conditional(InSet(b, Bit), And(InSet(b, Natural), And(LessEq(zero, b), LessEq(b, one)).with_total_ordering_style())))

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())

b \mapsto \left\{b \in \mathbb{N}^{\leq 1} \textrm{ if } b \in \mathbb{N} ,  0 \leq b \leq 1\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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