Expression of type Forall

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

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b, c], instance_expr = InSet(Lambda(x, Mod(Add(x, c), N)), Bijections(Interval(a, b), Interval(zero, subtract(N, one)))), domain = 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())

\forall_{a, b, c \in \mathbb{Z}}~\left(\left[x \mapsto \left(\left(x + c\right) ~\textup{mod}~ N\right)\right] \in \left[\{a~\ldotp \ldotp~b\} \xrightarrow[\text{onto}]{\text{1-to-1}} \{0~\ldotp \ldotp~N - 1\}\right]\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	34, 35, 39
5	Conditional	value: 6 condition: 7
6	Operation	operator: 22 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14, 15
11	Lambda	parameter: 38 body: 17
12	Operation	operator: 18 operands: 19
13	Operation	operator: 22 operands: 20
14	Operation	operator: 22 operands: 21
15	Operation	operator: 22 operands: 23
16	ExprTuple	38
17	Operation	operator: 24 operands: 25
18	Literal
19	ExprTuple	26, 27
20	ExprTuple	34, 28
21	ExprTuple	35, 28
22	Literal
23	ExprTuple	39, 28
24	Literal
25	ExprTuple	29, 42
26	Operation	operator: 31 operands: 30
27	Operation	operator: 31 operands: 32
28	Literal
29	Operation	operator: 40 operands: 33
30	ExprTuple	34, 35
31	Literal
32	ExprTuple	36, 37
33	ExprTuple	38, 39
34	Variable
35	Variable
36	Literal
37	Operation	operator: 40 operands: 41
38	Variable
39	Variable
40	Literal
41	ExprTuple	42, 43
42	Variable
43	Operation	operator: 44 operand: 46
44	Literal
45	ExprTuple	46
46	Literal