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 Forall, InSet
from proveit.numbers import Add, one, zero

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

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(0 \in S, \forall_{x \in S}~\left(\left(x + 1\right) \in S\right)\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: 13 operands: 3
2	Operation	operator: 4 operand: 7
3	ExprTuple	6, 16
4	Literal
5	ExprTuple	7
6	Literal
7	Lambda	parameter: 19 body: 9
8	ExprTuple	19
9	Conditional	value: 10 condition: 11
10	Operation	operator: 13 operands: 12
11	Operation	operator: 13 operands: 14
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	19, 16
15	Operation	operator: 17 operands: 18
16	Variable
17	Literal
18	ExprTuple	19, 20
19	Variable
20	Literal