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

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(P, Implies(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 \mapsto \left(\left(P\left(0\right) \land \left[\forall_{m \in \mathbb{N}~|~P\left(m\right)}~P\left(m + 1\right)\right]\right) \Rightarrow \left[\forall_{n \in \mathbb{N}}~P\left(n\right)\right]\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: 37 body: 3
2	ExprTuple	37
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 28 operands: 8
7	Operation	operator: 14 operand: 12
8	ExprTuple	10, 11
9	ExprTuple	12
10	Operation	operator: 37 operand: 17
11	Operation	operator: 14 operand: 18
12	Lambda	parameter: 26 body: 16
13	ExprTuple	17
14	Literal
15	ExprTuple	18
16	Conditional	value: 19 condition: 20
17	Literal
18	Lambda	parameter: 41 body: 21
19	Operation	operator: 37 operand: 26
20	Operation	operator: 35 operands: 23
21	Conditional	value: 24 condition: 25
22	ExprTuple	26
23	ExprTuple	26, 40
24	Operation	operator: 37 operand: 30
25	Operation	operator: 28 operands: 29
26	Variable
27	ExprTuple	30
28	Literal
29	ExprTuple	31, 32
30	Operation	operator: 33 operands: 34
31	Operation	operator: 35 operands: 36
32	Operation	operator: 37 operand: 41
33	Literal
34	ExprTuple	41, 39
35	Literal
36	ExprTuple	41, 40
37	Variable
38	ExprTuple	41
39	Literal
40	Literal
41	Variable