Expression of type Conditional

from the theory of proveit.linear_algebra.scalar_multiplication

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, V, x, y
from proveit.linear_algebra import binary_lin_comb_ax_by
from proveit.logic import And, InSet

# build up the expression from sub-expressions
expr = Conditional(InSet(binary_lin_comb_ax_by, V), And(InSet(x, V), InSet(y, 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(\left(a \cdot x\right) + \left(b \cdot y\right)\right) \in V \textrm{ if } x \in V ,  y \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: 12 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 16
4	Literal
5	ExprTuple	7, 8
6	Operation	operator: 9 operands: 10
7	Operation	operator: 12 operands: 11
8	Operation	operator: 12 operands: 13
9	Literal
10	ExprTuple	14, 15
11	ExprTuple	21, 16
12	Literal
13	ExprTuple	23, 16
14	Operation	operator: 18 operands: 17
15	Operation	operator: 18 operands: 19
16	Variable
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22, 23
20	Variable
21	Variable
22	Variable
23	Variable