Expression of type Equals

from the theory of proveit.logic.sets.enumeration

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 ExprRange, Function, IndexedVar, P, Px, Variable, a, n, x
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Equals, FALSE, Forall, Or, Set
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Or(ExprRange(sub_expr1, Equals(Function(P, [IndexedVar(a, sub_expr1)]), FALSE), one, n)), Equals(Forall(instance_param_or_params = [x], instance_expr = Px, domain = Set(a_1_to_n)), FALSE))

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(\left(P\left(a_{1}\right) = \bot\right) \lor  \left(P\left(a_{2}\right) = \bot\right) \lor  \ldots \lor  \left(P\left(a_{n}\right) = \bot\right)\right) = \left(\left[\forall_{x \in \left\{a_{1}, a_{2}, \ldots, a_{n}\right\}}~P\left(x\right)\right] = \bot\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',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 14 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 14 operands: 6
4	Literal
5	ExprTuple	7
6	ExprTuple	8, 18
7	ExprRange	lambda_map: 9 start_index: 32 end_index: 33
8	Operation	operator: 10 operand: 13
9	Lambda	parameter: 37 body: 12
10	Literal
11	ExprTuple	13
12	Operation	operator: 14 operands: 15
13	Lambda	parameter: 26 body: 16
14	Literal
15	ExprTuple	17, 18
16	Conditional	value: 19 condition: 20
17	Operation	operator: 22 operand: 34
18	Literal
19	Operation	operator: 22 operand: 26
20	Operation	operator: 24 operands: 25
21	ExprTuple	34
22	Variable
23	ExprTuple	26
24	Literal
25	ExprTuple	26, 27
26	Variable
27	Operation	operator: 28 operands: 29
28	Literal
29	ExprTuple	30
30	ExprRange	lambda_map: 31 start_index: 32 end_index: 33
31	Lambda	parameter: 37 body: 34
32	Literal
33	Variable
34	IndexedVar	variable: 35 index: 37
35	Variable
36	ExprTuple	37
37	Variable