Expression of type Lambda

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, Lambda, 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 = Lambda(v, 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())

v \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

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