Expression of type Equals

from the theory of proveit.linear_algebra.linear_maps

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 A, B, Conditional, Function, Lambda, V, x
from proveit.linear_algebra import VecAdd
from proveit.logic import Equals, InSet

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Equals(VecAdd(A, B), Lambda(x, Conditional(VecAdd(Function(A, sub_expr1), Function(B, sub_expr1)), InSet(x, V))))

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 + B\right) = \left[x \mapsto \left\{A\left(x\right) + B\left(x\right) \textrm{ if } x \in V\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	Operation	operator: 9 operands: 5
4	Lambda	parameter: 19 body: 6
5	ExprTuple	16, 17
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operands: 10
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13, 14
11	Literal
12	ExprTuple	19, 15
13	Operation	operator: 16 operand: 19
14	Operation	operator: 17 operand: 19
15	Variable
16	Variable
17	Variable
18	ExprTuple	19
19	Variable