Expression of type Equals

from the theory of proveit.core_expr_types.tuples

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, IndexedVar, Variable, a, n
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Exp, one, two

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Len(operands = [ExprRange(sub_expr1, ExprRange(sub_expr2, IndexedVar(a, [sub_expr1, sub_expr2]), one, n), one, n)]), Exp(n, two))

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(a_{1, 1}, a_{1, 2}, \ldots, a_{1, n}, a_{2, 1}, a_{2, 2}, \ldots, a_{2, n}, \ldots\ldots, a_{n, 1}, a_{n, 2}, \ldots, a_{n, n}\right)| = n^{2}

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 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	16, 10
9	ExprRange	lambda_map: 11 start_index: 15 end_index: 16
10	Literal
11	Lambda	parameter: 21 body: 13
12	ExprTuple	21
13	ExprRange	lambda_map: 14 start_index: 15 end_index: 16
14	Lambda	parameter: 22 body: 18
15	Literal
16	Variable
17	ExprTuple	22
18	IndexedVar	variable: 19 indices: 20
19	Variable
20	ExprTuple	21, 22
21	Variable
22	Variable