Expression of type Lambda

from the theory of proveit.numbers.modular

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, NotEquals
from proveit.numbers import Abs, Integer, Interval, ModAbs, one, subtract, zero

# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(InSet(ModAbs(a, b), Interval(zero, subtract(Abs(b), one))), And(InSet(a, Integer), InSet(b, Integer), 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|a\right|_{\textup{mod}\thinspace b} \in \{0~\ldotp \ldotp~\left|b\right| - 1\} \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  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: 13 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 17 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10, 11
7	Operation	operator: 12 operands: 13
8	Operation	operator: 14 operands: 15
9	Operation	operator: 17 operands: 16
10	Operation	operator: 17 operands: 18
11	Operation	operator: 19 operands: 20
12	Literal
13	ExprTuple	22, 33
14	Literal
15	ExprTuple	24, 21
16	ExprTuple	22, 23
17	Literal
18	ExprTuple	33, 23
19	Literal
20	ExprTuple	33, 24
21	Operation	operator: 25 operands: 26
22	Variable
23	Literal
24	Literal
25	Literal
26	ExprTuple	27, 28
27	Operation	operator: 29 operand: 33
28	Operation	operator: 31 operand: 34
29	Literal
30	ExprTuple	33
31	Literal
32	ExprTuple	34
33	Variable
34	Literal