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, m, n
from proveit.logic import And, Forall
from proveit.numbers import Natural, P_mAddOne, Pm, Pn, Pzero

# build up the expression from sub-expressions
expr = ExprTuple(And(Pzero, Forall(instance_param_or_params = [m], instance_expr = P_mAddOne, domain = Natural, condition = Pm)), Forall(instance_param_or_params = [n], instance_expr = Pn, domain = 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(P\left(0\right) \land \left[\forall_{m \in \mathbb{N}~|~P\left(m\right)}~P\left(m + 1\right)\right], \forall_{n \in \mathbb{N}}~P\left(n\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: 23 operands: 3
2	Operation	operator: 9 operand: 7
3	ExprTuple	5, 6
4	ExprTuple	7
5	Operation	operator: 32 operand: 12
6	Operation	operator: 9 operand: 13
7	Lambda	parameter: 21 body: 11
8	ExprTuple	12
9	Literal
10	ExprTuple	13
11	Conditional	value: 14 condition: 15
12	Literal
13	Lambda	parameter: 36 body: 16
14	Operation	operator: 32 operand: 21
15	Operation	operator: 30 operands: 18
16	Conditional	value: 19 condition: 20
17	ExprTuple	21
18	ExprTuple	21, 35
19	Operation	operator: 32 operand: 25
20	Operation	operator: 23 operands: 24
21	Variable
22	ExprTuple	25
23	Literal
24	ExprTuple	26, 27
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operands: 31
27	Operation	operator: 32 operand: 36
28	Literal
29	ExprTuple	36, 34
30	Literal
31	ExprTuple	36, 35
32	Variable
33	ExprTuple	36
34	Literal
35	Literal
36	Variable