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 L, x
from proveit.logic import Equals, Forall
from proveit.numbers import Interval, Mod, NaturalPos, one, subtract, zero

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [L], instance_expr = Forall(instance_param_or_params = [x], instance_expr = Equals(Mod(x, L), x), domain = Interval(zero, subtract(L, one))), domain = NaturalPos)

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_{L \in \mathbb{N}^+}~\left[\forall_{x \in \{0~\ldotp \ldotp~L - 1\}}~\left(\left(x ~\textup{mod}~ L\right) = x\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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 31 body: 4
3	ExprTuple	31
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 18 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	31, 11
10	Lambda	parameter: 26 body: 13
11	Literal
12	ExprTuple	26
13	Conditional	value: 14 condition: 15
14	Operation	operator: 16 operands: 17
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	20, 26
18	Literal
19	ExprTuple	26, 21
20	Operation	operator: 22 operands: 23
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	26, 31
24	Literal
25	ExprTuple	27, 28
26	Variable
27	Literal
28	Operation	operator: 29 operands: 30
29	Literal
30	ExprTuple	31, 32
31	Variable
32	Operation	operator: 33 operand: 35
33	Literal
34	ExprTuple	35
35	Literal