Expression of type Equals

from the theory of proveit.logic.sets.inclusion

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 x
from proveit.logic import Equals, Forall, InSet, Set, SubsetEq
from proveit.numbers import five, four, one, three, two

# build up the expression from sub-expressions
sub_expr1 = Set(one, three, five)
sub_expr2 = Set(one, two, three, four, five)
expr = Equals(SubsetEq(sub_expr1, sub_expr2), Forall(instance_param_or_params = [x], instance_expr = InSet(x, sub_expr2), domain = sub_expr1))

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\{1, 3, 5\right\} \subseteq \left\{1, 2, 3, 4, 5\right\}\right) = \left[\forall_{x \in \left\{1, 3, 5\right\}}~\left(x \in \left\{1, 2, 3, 4, 5\right\}\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',)
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: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operand: 9
5	Literal
6	ExprTuple	19, 17
7	Literal
8	ExprTuple	9
9	Lambda	parameter: 18 body: 11
10	ExprTuple	18
11	Conditional	value: 12 condition: 13
12	Operation	operator: 15 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	18, 17
15	Literal
16	ExprTuple	18, 19
17	Operation	operator: 21 operands: 20
18	Variable
19	Operation	operator: 21 operands: 22
20	ExprTuple	25, 23, 26, 24, 27
21	Literal
22	ExprTuple	25, 26, 27
23	Literal
24	Literal
25	Literal
26	Literal
27	Literal