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

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(S, Conditional(Implies(And(InSet(zero, S), Forall(instance_param_or_params = [x], instance_expr = InSet(Add(x, one), S), domain = S)), SetEquiv(S, Natural)), SubsetEq(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(S \mapsto \left\{\left(\left(0 \in S\right) \land \left[\forall_{x \in S}~\left(\left(x + 1\right) \in S\right)\right]\right) \Rightarrow \left(S \cong \mathbb{N}\right) \textrm{ if } S \subseteq \mathbb{N}\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	parameter: 31 body: 3
2	ExprTuple	31
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 14
6	Literal
7	ExprTuple	9, 10
8	Literal
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	31, 17
15	Operation	operator: 28 operands: 18
16	Operation	operator: 19 operand: 22
17	Literal
18	ExprTuple	21, 31
19	Literal
20	ExprTuple	22
21	Literal
22	Lambda	parameter: 34 body: 24
23	ExprTuple	34
24	Conditional	value: 25 condition: 26
25	Operation	operator: 28 operands: 27
26	Operation	operator: 28 operands: 29
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	34, 31
30	Operation	operator: 32 operands: 33
31	Variable
32	Literal
33	ExprTuple	34, 35
34	Variable
35	Literal