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

# build up the expression from sub-expressions
expr = Lambda(c, Conditional(Forall(instance_param_or_params = [x], instance_expr = Equals(Function(P, [ScalarMult(c, x)]), ScalarMult(c, Px)), domain = V), InSet(c, K)))

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())

c \mapsto \left\{\forall_{x \in V}~\left(P\left(c \cdot x\right) = \left(c \cdot P\left(x\right)\right)\right) \textrm{ if } c \in K\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 28 body: 2
1	ExprTuple	28
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 15 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	28, 9
8	Lambda	parameter: 29 body: 10
9	Variable
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operands: 14
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	29, 19
17	Operation	operator: 26 operand: 22
18	Operation	operator: 24 operands: 21
19	Variable
20	ExprTuple	22
21	ExprTuple	28, 23
22	Operation	operator: 24 operands: 25
23	Operation	operator: 26 operand: 29
24	Literal
25	ExprTuple	28, 29
26	Variable
27	ExprTuple	29
28	Variable
29	Variable