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, b, m
from proveit.logic import And, Equals
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)
sub_expr3 = ExprRange(sub_expr1, IndexedVar(a, sub_expr1), one, m)
sub_expr4 = IndexedVar(a, sub_expr2)
sub_expr5 = ExprRange(sub_expr1, IndexedVar(b, sub_expr1), one, m)
sub_expr6 = IndexedVar(b, sub_expr2)
expr = Equals(Equals([sub_expr3, sub_expr4], [sub_expr5, sub_expr6]), And(Equals([sub_expr3], [sub_expr5]), Equals(sub_expr4, sub_expr6))).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \left(\left(a_{1}, a_{2}, \ldots, a_{m}, a_{m + 1}\right) = \left(b_{1}, b_{2}, \ldots, b_{m}, b_{m + 1}\right)\right) =  \\ \left(\left(\left(a_{1}, a_{2}, \ldots, a_{m}\right) = \left(b_{1}, b_{2}, \ldots, b_{m}\right)\right) \land \left(a_{m + 1} = b_{m + 1}\right)\right) \end{array} \end{array}

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.	()	(2)	('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: 12 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 12 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	ExprTuple	18, 16
8	ExprTuple	19, 17
9	Operation	operator: 12 operands: 11
10	Operation	operator: 12 operands: 13
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16, 17
14	ExprTuple	18
15	ExprTuple	19
16	IndexedVar	variable: 28 index: 23
17	IndexedVar	variable: 29 index: 23
18	ExprRange	lambda_map: 21 start_index: 32 end_index: 31
19	ExprRange	lambda_map: 22 start_index: 32 end_index: 31
20	ExprTuple	23
21	Lambda	parameter: 33 body: 24
22	Lambda	parameter: 33 body: 25
23	Operation	operator: 26 operands: 27
24	IndexedVar	variable: 28 index: 33
25	IndexedVar	variable: 29 index: 33
26	Literal
27	ExprTuple	31, 32
28	Variable
29	Variable
30	ExprTuple	33
31	Variable
32	Literal
33	Variable