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, N, a, b, c, x
from proveit.logic import And, Bijections, InSet
from proveit.numbers import Integer, Interval, Mod, one, subtract, zero

# build up the expression from sub-expressions
expr = Lambda([a, b, c], Conditional(InSet(Lambda(x, Mod(x, N)), Bijections(Interval(a, b), Interval(zero, subtract(N, one)))), And(InSet(a, Integer), InSet(b, Integer), InSet(c, Integer))))

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, c\right) \mapsto \left\{\left[x \mapsto \left(x ~\textup{mod}~ N\right)\right] \in \left[\{a~\ldotp \ldotp~b\} \xrightarrow[\text{onto}]{\text{1-to-1}} \{0~\ldotp \ldotp~N - 1\}\right] \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  c \in \mathbb{Z}\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	31, 32, 25
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	Lambda	parameter: 27 body: 14
9	Operation	operator: 15 operands: 16
10	Operation	operator: 19 operands: 17
11	Operation	operator: 19 operands: 18
12	Operation	operator: 19 operands: 20
13	ExprTuple	27
14	Operation	operator: 21 operands: 22
15	Literal
16	ExprTuple	23, 24
17	ExprTuple	31, 26
18	ExprTuple	32, 26
19	Literal
20	ExprTuple	25, 26
21	Literal
22	ExprTuple	27, 37
23	Operation	operator: 29 operands: 28
24	Operation	operator: 29 operands: 30
25	Variable
26	Literal
27	Variable
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	33, 34
31	Variable
32	Variable
33	Literal
34	Operation	operator: 35 operands: 36
35	Literal
36	ExprTuple	37, 38
37	Variable
38	Operation	operator: 39 operand: 41
39	Literal
40	ExprTuple	41
41	Literal