Expression of type And

from the theory of proveit.logic.booleans.disjunction

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.core_expr_types import A_1_to_m
from proveit.logic import And, Boolean, Forall, InSet, Or
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = And(InSet(m, NaturalPos), Forall(instance_param_or_params = [A_1_to_m], instance_expr = InSet(Or(A_1_to_m), Boolean), domain = Boolean))

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(m \in \mathbb{N}^+\right) \land \left[\forall_{A_{1}, A_{2}, \ldots, A_{m} \in \mathbb{B}}~\left(\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m}\right) \in \mathbb{B}\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: 25 operands: 4
3	Operation	operator: 5 operand: 8
4	ExprTuple	24, 7
5	Literal
6	ExprTuple	8
7	Literal
8	Lambda	parameters: 18 body: 9
9	Conditional	value: 10 condition: 11
10	Operation	operator: 25 operands: 12
11	Operation	operator: 13 operands: 14
12	ExprTuple	15, 28
13	Literal
14	ExprTuple	16
15	Operation	operator: 17 operands: 18
16	ExprRange	lambda_map: 19 start_index: 23 end_index: 24
17	Literal
18	ExprTuple	20
19	Lambda	parameter: 31 body: 21
20	ExprRange	lambda_map: 22 start_index: 23 end_index: 24
21	Operation	operator: 25 operands: 26
22	Lambda	parameter: 31 body: 27
23	Literal
24	Variable
25	Literal
26	ExprTuple	27, 28
27	IndexedVar	variable: 29 index: 31
28	Literal
29	Variable
30	ExprTuple	31
31	Variable