Expression of type Lambda

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, Lambda, 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 = Lambda([x, y], 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(x, y\right) \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	23, 25
2	Conditional	value: 3 condition: 4
3	Operation	operator: 14 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 18
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	Literal
12	ExprTuple	16, 17
13	ExprTuple	23, 18
14	Literal
15	ExprTuple	25, 18
16	Operation	operator: 20 operands: 19
17	Operation	operator: 20 operands: 21
18	Variable
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25
22	Variable
23	Variable
24	Variable
25	Variable