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.core_expr_types import Len
from proveit.logic import 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)
expr = Equals(Len(operands = [ExprRange(sub_expr1, Equals(IndexedVar(a, sub_expr1), IndexedVar(b, sub_expr1)), one, m), Equals(IndexedVar(a, sub_expr2), IndexedVar(b, sub_expr2))]), 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} = b_{1}\right), \left(a_{2} = b_{2}\right), \ldots, \left(a_{m} = b_{m}\right), a_{m + 1} = b_{m + 1}\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: 16 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 5 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9
7	ExprRange	lambda_map: 10 start_index: 29 end_index: 28
8	Operation	operator: 16 operands: 11
9	ExprRange	lambda_map: 12 start_index: 29 end_index: 21
10	Lambda	parameter: 27 body: 13
11	ExprTuple	14, 15
12	Lambda	parameter: 27 body: 27
13	Operation	operator: 16 operands: 17
14	IndexedVar	variable: 22 index: 21
15	IndexedVar	variable: 23 index: 21
16	Literal
17	ExprTuple	19, 20
18	ExprTuple	21
19	IndexedVar	variable: 22 index: 27
20	IndexedVar	variable: 23 index: 27
21	Operation	operator: 25 operands: 26
22	Variable
23	Variable
24	ExprTuple	27
25	Literal
26	ExprTuple	28, 29
27	Variable
28	Variable
29	Literal