Expression of type Lambda

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 Conditional, Lambda, V, x
from proveit.linear_algebra import Identity
from proveit.logic import Equals, InSet

# build up the expression from sub-expressions
expr = Lambda(V, Equals(Identity(V), Lambda(x, Conditional(x, 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())

V \mapsto \left(I_{V} = \left[x \mapsto \left\{x \textrm{ if } x \in V\right..\right]\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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