Expression of type And

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)
expr = And(Equals([ExprRange(sub_expr1, IndexedVar(a, sub_expr1), one, m)], [ExprRange(sub_expr1, IndexedVar(b, sub_expr1), one, m)]), Equals(IndexedVar(a, sub_expr2), IndexedVar(b, 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}, 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)

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',)

# 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, 11
8	ExprTuple	12
9	ExprTuple	13
10	IndexedVar	variable: 22 index: 17
11	IndexedVar	variable: 23 index: 17
12	ExprRange	lambda_map: 15 start_index: 26 end_index: 25
13	ExprRange	lambda_map: 16 start_index: 26 end_index: 25
14	ExprTuple	17
15	Lambda	parameter: 27 body: 18
16	Lambda	parameter: 27 body: 19
17	Operation	operator: 20 operands: 21
18	IndexedVar	variable: 22 index: 27
19	IndexedVar	variable: 23 index: 27
20	Literal
21	ExprTuple	25, 26
22	Variable
23	Variable
24	ExprTuple	27
25	Variable
26	Literal
27	Variable