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 NaturalPos, P_mAddOne, Pm, Pn, Pone

# build up the expression from sub-expressions
expr = ExprTuple(And(Pone, Forall(instance_param_or_params = [m], instance_expr = P_mAddOne, domain = NaturalPos, condition = Pm)), Forall(instance_param_or_params = [n], instance_expr = Pn, domain = NaturalPos))

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(1\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: 22 operands: 3
2	Operation	operator: 9 operand: 7
3	ExprTuple	5, 6
4	ExprTuple	7
5	Operation	operator: 31 operand: 33
6	Operation	operator: 9 operand: 12
7	Lambda	parameter: 20 body: 11
8	ExprTuple	33
9	Literal
10	ExprTuple	12
11	Conditional	value: 13 condition: 14
12	Lambda	parameter: 35 body: 15
13	Operation	operator: 31 operand: 20
14	Operation	operator: 29 operands: 17
15	Conditional	value: 18 condition: 19
16	ExprTuple	20
17	ExprTuple	20, 34
18	Operation	operator: 31 operand: 24
19	Operation	operator: 22 operands: 23
20	Variable
21	ExprTuple	24
22	Literal
23	ExprTuple	25, 26
24	Operation	operator: 27 operands: 28
25	Operation	operator: 29 operands: 30
26	Operation	operator: 31 operand: 35
27	Literal
28	ExprTuple	35, 33
29	Literal
30	ExprTuple	35, 34
31	Variable
32	ExprTuple	35
33	Literal
34	Literal
35	Variable