Expression of type And

from the theory of proveit.linear_algebra.addition

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 V, a, b
from proveit.linear_algebra import InnerProd
from proveit.logic import And, Equals, InSet
from proveit.numbers import zero

# build up the expression from sub-expressions
expr = And(InSet(a, V), InSet(b, V), Equals(InnerProd(a, b), zero))

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 \in V\right) \land \left(b \in V\right) \land \left(\left \langle a, b\right \rangle = 0\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, 5
3	Operation	operator: 7 operands: 6
4	Operation	operator: 7 operands: 8
5	Operation	operator: 9 operands: 10
6	ExprTuple	16, 11
7	Literal
8	ExprTuple	17, 11
9	Literal
10	ExprTuple	12, 13
11	Variable
12	Operation	operator: 14 operands: 15
13	Literal
14	Literal
15	ExprTuple	16, 17
16	Variable
17	Variable