Expression of type Conditional

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 Conditional, a, b, p
from proveit.logic import And, InSet, Not
from proveit.numbers import Divides, NaturalPos, greater, one

# build up the expression from sub-expressions
expr = Conditional(Not(And(Divides(p, a), Divides(p, b))), And(InSet(p, NaturalPos), 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())

\left\{\lnot \left(\left(p \rvert a\right) \land \left(p \rvert b\right)\right) \textrm{ if } p \in \mathbb{N}^+ ,  p > 1\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 9 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Operation	operator: 9 operands: 10
7	Operation	operator: 11 operands: 12
8	Operation	operator: 13 operands: 14
9	Literal
10	ExprTuple	15, 16
11	Literal
12	ExprTuple	23, 17
13	Literal
14	ExprTuple	18, 23
15	Operation	operator: 20 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	23, 22
20	Literal
21	ExprTuple	23, 24
22	Variable
23	Variable
24	Variable