Expression of type Lambda

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, Lambda, 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 = Lambda([a, b], 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(a, b\right) \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 24 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operand: 7
3	Operation	operator: 28 operands: 6
4	Literal
5	ExprTuple	7
6	ExprTuple	8, 9, 10
7	Lambda	parameter: 42 body: 12
8	Operation	operator: 30 operands: 13
9	Operation	operator: 30 operands: 14
10	Operation	operator: 15 operands: 16
11	ExprTuple	42
12	Conditional	value: 17 condition: 18
13	ExprTuple	41, 36
14	ExprTuple	43, 36
15	Literal
16	ExprTuple	19, 37
17	Operation	operator: 20 operand: 25
18	Operation	operator: 28 operands: 22
19	Operation	operator: 23 operands: 24
20	Literal
21	ExprTuple	25
22	ExprTuple	26, 27
23	Literal
24	ExprTuple	41, 43
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operands: 31
27	Operation	operator: 32 operands: 33
28	Literal
29	ExprTuple	34, 35
30	Literal
31	ExprTuple	42, 36
32	Literal
33	ExprTuple	37, 42
34	Operation	operator: 39 operands: 38
35	Operation	operator: 39 operands: 40
36	Literal
37	Literal
38	ExprTuple	42, 41
39	Literal
40	ExprTuple	42, 43
41	Variable
42	Variable
43	Variable