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, K, Lambda, P, Px, V, W, c, x
from proveit.linear_algebra import LinMap, ScalarMult, VecSpaces
from proveit.logic import And, Equals, Forall, InClass, InSet

# build up the expression from sub-expressions
sub_expr1 = VecSpaces(K)
expr = Lambda([V, W], Conditional(Forall(instance_param_or_params = [c], instance_expr = Forall(instance_param_or_params = [P], instance_expr = Equals(ScalarMult(c, P), Lambda(x, Conditional(ScalarMult(c, Px), InSet(x, V)))), domain = LinMap(V, W)), domain = K), And(InClass(V, sub_expr1), InClass(W, sub_expr1))))

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(V, W\right) \mapsto \left\{\forall_{c \in K}~\left[\forall_{P \in \mathcal{L}\left(V, W\right)}~\left(\left(c \cdot P\right) = \left[x \mapsto \left\{c \cdot P\left(x\right) \textrm{ if } x \in V\right..\right]\right)\right] \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right) ,  W \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 38 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 18 operand: 7
3	Operation	operator: 5 operands: 6
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameter: 46 body: 11
8	Operation	operator: 13 operands: 12
9	Operation	operator: 13 operands: 14
10	ExprTuple	46
11	Conditional	value: 15 condition: 16
12	ExprTuple	48, 17
13	Literal
14	ExprTuple	41, 17
15	Operation	operator: 18 operand: 23
16	Operation	operator: 44 operands: 20
17	Operation	operator: 21 operand: 24
18	Literal
19	ExprTuple	23
20	ExprTuple	46, 24
21	Literal
22	ExprTuple	24
23	Lambda	parameter: 49 body: 26
24	Variable
25	ExprTuple	49
26	Conditional	value: 27 condition: 28
27	Operation	operator: 29 operands: 30
28	Operation	operator: 44 operands: 31
29	Literal
30	ExprTuple	32, 33
31	ExprTuple	49, 34
32	Operation	operator: 42 operands: 35
33	Lambda	parameter: 51 body: 36
34	Operation	operator: 37 operands: 38
35	ExprTuple	46, 49
36	Conditional	value: 39 condition: 40
37	Literal
38	ExprTuple	48, 41
39	Operation	operator: 42 operands: 43
40	Operation	operator: 44 operands: 45
41	Variable
42	Literal
43	ExprTuple	46, 47
44	Literal
45	ExprTuple	51, 48
46	Variable
47	Operation	operator: 49 operand: 51
48	Variable
49	Variable
50	ExprTuple	51
51	Variable