Expression of type And

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

# build up the expression from sub-expressions
expr = And(Pzero, Forall(instance_param_or_params = [m], instance_expr = P_mAddOne, domain = Natural, condition = Pm))

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())

P\left(0\right) \land \left[\forall_{m \in \mathbb{N}~|~P\left(m\right)}~P\left(m + 1\right)\right]

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 13 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 22 operand: 7
3	Operation	operator: 5 operand: 8
4	ExprTuple	7
5	Literal
6	ExprTuple	8
7	Literal
8	Lambda	parameter: 26 body: 9
9	Conditional	value: 10 condition: 11
10	Operation	operator: 22 operand: 15
11	Operation	operator: 13 operands: 14
12	ExprTuple	15
13	Literal
14	ExprTuple	16, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Operation	operator: 22 operand: 26
18	Literal
19	ExprTuple	26, 24
20	Literal
21	ExprTuple	26, 25
22	Variable
23	ExprTuple	26
24	Literal
25	Literal
26	Variable