Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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(\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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 25 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 29 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10, 11
8	Lambda	parameter: 43 body: 13
9	Operation	operator: 31 operands: 14
10	Operation	operator: 31 operands: 15
11	Operation	operator: 16 operands: 17
12	ExprTuple	43
13	Conditional	value: 18 condition: 19
14	ExprTuple	42, 37
15	ExprTuple	44, 37
16	Literal
17	ExprTuple	20, 38
18	Operation	operator: 21 operand: 26
19	Operation	operator: 29 operands: 23
20	Operation	operator: 24 operands: 25
21	Literal
22	ExprTuple	26
23	ExprTuple	27, 28
24	Literal
25	ExprTuple	42, 44
26	Operation	operator: 29 operands: 30
27	Operation	operator: 31 operands: 32
28	Operation	operator: 33 operands: 34
29	Literal
30	ExprTuple	35, 36
31	Literal
32	ExprTuple	43, 37
33	Literal
34	ExprTuple	38, 43
35	Operation	operator: 40 operands: 39
36	Operation	operator: 40 operands: 41
37	Literal
38	Literal
39	ExprTuple	43, 42
40	Literal
41	ExprTuple	43, 44
42	Variable
43	Variable
44	Variable