Expression of type Conditional ¶

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 = 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)))

# 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\{\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()

# display the expression information
stored_expr.expr_info()

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

Expression of type Conditional¶

from the theory of proveit.linear_algebra.linear_maps¶

Expression of type Conditional ¶

from the theory of proveit.linear_algebra.linear_maps ¶