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 A, B, Conditional, Function, K, Lambda, V, W, x
from proveit.linear_algebra import LinMap, VecAdd, VecSpaces
from proveit.logic import And, Equals, Forall, InClass, InSet

# build up the expression from sub-expressions
sub_expr1 = [x]
sub_expr2 = VecSpaces(K)
expr = Conditional(Forall(instance_param_or_params = [A, B], instance_expr = Equals(VecAdd(A, B), Lambda(x, Conditional(VecAdd(Function(A, sub_expr1), Function(B, sub_expr1)), InSet(x, V)))), domain = LinMap(V, W)), And(InClass(V, sub_expr2), InClass(W, sub_expr2)))

# 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_{A, B \in \mathcal{L}\left(V, W\right)}~\left(\left(A + B\right) = \left[x \mapsto \left\{A\left(x\right) + B\left(x\right) \textrm{ if } x \in V\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: 3 operand: 6
2	Operation	operator: 18 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameters: 27 body: 9
7	Operation	operator: 11 operands: 10
8	Operation	operator: 11 operands: 12
9	Conditional	value: 13 condition: 14
10	ExprTuple	42, 15
11	Literal
12	ExprTuple	43, 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	Operation	operator: 20 operand: 26
16	Literal
17	ExprTuple	22, 23
18	Literal
19	ExprTuple	24, 25
20	Literal
21	ExprTuple	26
22	Operation	operator: 34 operands: 27
23	Lambda	parameter: 47 body: 28
24	Operation	operator: 36 operands: 29
25	Operation	operator: 36 operands: 30
26	Variable
27	ExprTuple	44, 45
28	Conditional	value: 31 condition: 32
29	ExprTuple	44, 33
30	ExprTuple	45, 33
31	Operation	operator: 34 operands: 35
32	Operation	operator: 36 operands: 37
33	Operation	operator: 38 operands: 39
34	Literal
35	ExprTuple	40, 41
36	Literal
37	ExprTuple	47, 42
38	Literal
39	ExprTuple	42, 43
40	Operation	operator: 44 operand: 47
41	Operation	operator: 45 operand: 47
42	Variable
43	Variable
44	Variable
45	Variable
46	ExprTuple	47
47	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 ¶