Expression of type Conditional

from the theory of proveit.linear_algebra

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 Conditional, Function, S, T, V, v
from proveit.linear_algebra import LinMapAdd
from proveit.logic import Equals, InSet
from proveit.numbers import Add

# build up the expression from sub-expressions
sub_expr1 = [v]
expr = Conditional(Equals(Function(LinMapAdd(S, T), sub_expr1), Add(Function(S, sub_expr1), Function(T, sub_expr1))), InSet(v, 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\{\left(S + T\right)\left(v\right) = \left(S\left(v\right) + T\left(v\right)\right) \textrm{ if } v \in V\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	20, 9
7	Operation	operator: 10 operand: 20
8	Operation	operator: 11 operands: 12
9	Variable
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17, 18
15	Operation	operator: 17 operand: 20
16	Operation	operator: 18 operand: 20
17	Variable
18	Variable
19	ExprTuple	20
20	Variable