Expression of type Forall

from the theory of proveit.numbers.divisibility

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, p
from proveit.logic import And, Forall, Not
from proveit.numbers import Divides, NaturalPos, greater, one

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [p], instance_expr = Not(And(Divides(p, a), Divides(p, b))), domain = NaturalPos, condition = greater(p, one))

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_{p \in \mathbb{N}^+~|~p > 1}~(\lnot \left(\left(p \rvert a\right) \land \left(p \rvert b\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	parameter: 28 body: 5
4	ExprTuple	28
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operand: 11
7	Operation	operator: 14 operands: 10
8	Literal
9	ExprTuple	11
10	ExprTuple	12, 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	Operation	operator: 18 operands: 19
14	Literal
15	ExprTuple	20, 21
16	Literal
17	ExprTuple	28, 22
18	Literal
19	ExprTuple	23, 28
20	Operation	operator: 25 operands: 24
21	Operation	operator: 25 operands: 26
22	Literal
23	Literal
24	ExprTuple	28, 27
25	Literal
26	ExprTuple	28, 29
27	Variable
28	Variable
29	Variable