Expression of type Equals

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 A, ExprRange, IndexedVar, Variable, m
from proveit.core_expr_types import Len
from proveit.logic import Boolean, Equals, InSet
from proveit.numbers import Add, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(m, one)
expr = Equals(Len(operands = [ExprRange(sub_expr1, InSet(IndexedVar(A, sub_expr1), Boolean), one, m), InSet(IndexedVar(A, sub_expr2), Boolean)]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, sub_expr2)]))

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(A_{1} \in \mathbb{B}\right), \left(A_{2} \in \mathbb{B}\right), \ldots, \left(A_{m} \in \mathbb{B}\right), A_{m + 1} \in \mathbb{B}\right)| = |\left(1, 2, \ldots, \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',)
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: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10
8	ExprRange	lambda_map: 11 start_index: 28 end_index: 27
9	Operation	operator: 16 operands: 12
10	ExprRange	lambda_map: 13 start_index: 28 end_index: 21
11	Lambda	parameter: 26 body: 14
12	ExprTuple	15, 20
13	Lambda	parameter: 26 body: 26
14	Operation	operator: 16 operands: 17
15	IndexedVar	variable: 22 index: 21
16	Literal
17	ExprTuple	19, 20
18	ExprTuple	21
19	IndexedVar	variable: 22 index: 26
20	Literal
21	Operation	operator: 24 operands: 25
22	Variable
23	ExprTuple	26
24	Literal
25	ExprTuple	27, 28
26	Variable
27	Variable
28	Literal