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 Equals, Forall, InSet

# build up the expression from sub-expressions
expr = Lambda(K, Forall(instance_param_or_params = [V, W], instance_expr = 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), domain = VecSpaces(K)))

# 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())

K \mapsto \left[\forall_{V, W \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\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]\right]\right]

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Lambda	parameter: 27 body: 1
1	Operation	operator: 21 operand: 3
2	ExprTuple	3
3	Lambda	parameters: 41 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 21 operand: 10
6	Operation	operator: 8 operands: 9
7	ExprTuple	10
8	Literal
9	ExprTuple	11, 12
10	Lambda	parameter: 49 body: 14
11	Operation	operator: 16 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprTuple	49
14	Conditional	value: 18 condition: 19
15	ExprTuple	51, 20
16	Literal
17	ExprTuple	44, 20
18	Operation	operator: 21 operand: 26
19	Operation	operator: 47 operands: 23
20	Operation	operator: 24 operand: 27
21	Literal
22	ExprTuple	26
23	ExprTuple	49, 27
24	Literal
25	ExprTuple	27
26	Lambda	parameter: 52 body: 29
27	Variable
28	ExprTuple	52
29	Conditional	value: 30 condition: 31
30	Operation	operator: 32 operands: 33
31	Operation	operator: 47 operands: 34
32	Literal
33	ExprTuple	35, 36
34	ExprTuple	52, 37
35	Operation	operator: 45 operands: 38
36	Lambda	parameter: 54 body: 39
37	Operation	operator: 40 operands: 41
38	ExprTuple	49, 52
39	Conditional	value: 42 condition: 43
40	Literal
41	ExprTuple	51, 44
42	Operation	operator: 45 operands: 46
43	Operation	operator: 47 operands: 48
44	Variable
45	Literal
46	ExprTuple	49, 50
47	Literal
48	ExprTuple	54, 51
49	Variable
50	Operation	operator: 52 operand: 54
51	Variable
52	Variable
53	ExprTuple	54
54	Variable

Expression of type Lambda¶

from the theory of proveit.linear_algebra.linear_maps¶

Expression of type Lambda ¶

from the theory of proveit.linear_algebra.linear_maps ¶