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 a, b, c
from proveit.logic import Forall, NotEquals
from proveit.numbers import Abs, Add, LessEq, Mod, ModAbs, Real, subtract, zero

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b, c], instance_expr = LessEq(ModAbs(subtract(Mod(Add(b, a), c), b), c), Abs(a)), domain = Real, condition = NotEquals(c, 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())

\forall_{a, b, c \in \mathbb{R}~|~c \neq 0}~\left(\left|\left(\left(b + a\right) ~\textup{mod}~ c\right) - b\right|_{\textup{mod}\thinspace c} \leq \left|a\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	43, 42, 39
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15, 16, 17
12	Operation	operator: 18 operands: 19
13	Operation	operator: 20 operand: 43
14	Operation	operator: 24 operands: 22
15	Operation	operator: 24 operands: 23
16	Operation	operator: 24 operands: 25
17	Operation	operator: 26 operands: 27
18	Literal
19	ExprTuple	28, 39
20	Literal
21	ExprTuple	43
22	ExprTuple	43, 29
23	ExprTuple	42, 29
24	Literal
25	ExprTuple	39, 29
26	Literal
27	ExprTuple	39, 30
28	Operation	operator: 40 operands: 31
29	Literal
30	Literal
31	ExprTuple	32, 33
32	Operation	operator: 34 operands: 35
33	Operation	operator: 36 operand: 42
34	Literal
35	ExprTuple	38, 39
36	Literal
37	ExprTuple	42
38	Operation	operator: 40 operands: 41
39	Variable
40	Literal
41	ExprTuple	42, 43
42	Variable
43	Variable