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, Function, Variable, f, i, j, m, n
from proveit.logic import Equals

# 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([ExprRange(sub_expr1, ExprRange(sub_expr2, Function(f, [sub_expr1, sub_expr2]), i, j), m, n)], [])

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(f\left(m, i\right), f\left(m, i + 1\right), \ldots, f\left(m, j\right), f\left(m + 1, i\right), f\left(m + 1, i + 1\right), \ldots, f\left(m + 1, j\right), \ldots\ldots, f\left(n, i\right), f\left(n, i + 1\right), \ldots, f\left(n, j\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	ExprTuple	5
4	ExprTuple
5	ExprRange	lambda_map: 6 start_index: 7 end_index: 8
6	Lambda	parameter: 18 body: 10
7	Variable
8	Variable
9	ExprTuple	18
10	ExprRange	lambda_map: 11 start_index: 12 end_index: 13
11	Lambda	parameter: 19 body: 15
12	Variable
13	Variable
14	ExprTuple	19
15	Operation	operator: 16 operands: 17
16	Variable
17	ExprTuple	18, 19
18	Variable
19	Variable