Expression of type ExprTuple

from the theory of proveit.numbers.number_sets.natural_numbers

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 ExprTuple, S, x
from proveit.logic import And, Forall, InSet, SetEquiv
from proveit.numbers import Add, Natural, one, zero

# build up the expression from sub-expressions
expr = ExprTuple(And(InSet(zero, S), Forall(instance_param_or_params = [x], instance_expr = InSet(Add(x, one), S), domain = S)), SetEquiv(S, Natural))

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(0 \in S\right) \land \left[\forall_{x \in S}~\left(\left(x + 1\right) \in S\right)\right], S \cong \mathbb{N}\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	23, 9
7	Operation	operator: 20 operands: 10
8	Operation	operator: 11 operand: 14
9	Literal
10	ExprTuple	13, 23
11	Literal
12	ExprTuple	14
13	Literal
14	Lambda	parameter: 26 body: 16
15	ExprTuple	26
16	Conditional	value: 17 condition: 18
17	Operation	operator: 20 operands: 19
18	Operation	operator: 20 operands: 21
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	26, 23
22	Operation	operator: 24 operands: 25
23	Variable
24	Literal
25	ExprTuple	26, 27
26	Variable
27	Literal