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, Equals, Forall, InSet, Not
from proveit.numbers import Divides, GCD, NaturalPos, greater, one

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [p], instance_expr = Not(And(Divides(p, a), Divides(p, b))), domain = NaturalPos, condition = greater(p, one)), And(InSet(a, NaturalPos), InSet(b, NaturalPos), Equals(GCD(a, b), 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\{\forall_{p \in \mathbb{N}^+~|~p > 1}~(\lnot \left(\left(p \rvert a\right) \land \left(p \rvert b\right)\right)) \textrm{ if } a \in \mathbb{N}^+ ,  b \in \mathbb{N}^+ ,  gcd\left(a, b\right) = 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: 27 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8, 9
6	Lambda	parameter: 41 body: 11
7	Operation	operator: 29 operands: 12
8	Operation	operator: 29 operands: 13
9	Operation	operator: 14 operands: 15
10	ExprTuple	41
11	Conditional	value: 16 condition: 17
12	ExprTuple	40, 35
13	ExprTuple	42, 35
14	Literal
15	ExprTuple	18, 36
16	Operation	operator: 19 operand: 24
17	Operation	operator: 27 operands: 21
18	Operation	operator: 22 operands: 23
19	Literal
20	ExprTuple	24
21	ExprTuple	25, 26
22	Literal
23	ExprTuple	40, 42
24	Operation	operator: 27 operands: 28
25	Operation	operator: 29 operands: 30
26	Operation	operator: 31 operands: 32
27	Literal
28	ExprTuple	33, 34
29	Literal
30	ExprTuple	41, 35
31	Literal
32	ExprTuple	36, 41
33	Operation	operator: 38 operands: 37
34	Operation	operator: 38 operands: 39
35	Literal
36	Literal
37	ExprTuple	41, 40
38	Literal
39	ExprTuple	41, 42
40	Variable
41	Variable
42	Variable