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, Function, Lambda, P, Px, V, c, x
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, InSet

# build up the expression from sub-expressions
expr = Lambda(x, Conditional(Equals(Function(P, [ScalarMult(c, x)]), ScalarMult(c, Px)), 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())

x \mapsto \left\{P\left(c \cdot x\right) = \left(c \cdot P\left(x\right)\right) \textrm{ if } x \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: 20 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	20, 10
8	Operation	operator: 17 operand: 13
9	Operation	operator: 15 operands: 12
10	Variable
11	ExprTuple	13
12	ExprTuple	19, 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operand: 20
15	Literal
16	ExprTuple	19, 20
17	Variable
18	ExprTuple	20
19	Variable
20	Variable