Expression of type Lambda ¶

from the theory of proveit.linear_algebra.addition ¶

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, V, a, b
from proveit.linear_algebra import InnerProd, Norm, VecAdd, VecSpaces
from proveit.logic import Equals, Forall, InClass
from proveit.numbers import Add, Exp, sqrt, two, zero

# build up the expression from sub-expressions
expr = Lambda(V, Conditional(Forall(instance_param_or_params = [a, b], instance_expr = Equals(Norm(VecAdd(a, b)), sqrt(Add(Exp(Norm(a), two), Exp(Norm(b), two)))), domain = V, condition = Equals(InnerProd(a, b), zero)), InClass(V, 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())

V \mapsto \left\{\forall_{a, b \in V~|~\left \langle a, b\right \rangle = 0}~\left(\left \|a + b\right \| = \sqrt{\left(\left \|a\right \|^{2} + \left \|b\right \|^{2}\right)}\right) \textrm{ if } V \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	Lambda	parameter: 35 body: 2
1	ExprTuple	35
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	35, 10
9	Lambda	parameters: 44 body: 11
10	Operation	operator: 12 operand: 16
11	Conditional	value: 14 condition: 15
12	Literal
13	ExprTuple	16
14	Operation	operator: 30 operands: 17
15	Operation	operator: 18 operands: 19
16	Variable
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22, 23, 24
20	Operation	operator: 55 operand: 32
21	Operation	operator: 49 operands: 26
22	Operation	operator: 28 operands: 27
23	Operation	operator: 28 operands: 29
24	Operation	operator: 30 operands: 31
25	ExprTuple	32
26	ExprTuple	33, 34
27	ExprTuple	57, 35
28	Literal
29	ExprTuple	58, 35
30	Literal
31	ExprTuple	36, 37
32	Operation	operator: 38 operands: 44
33	Operation	operator: 39 operands: 40
34	Operation	operator: 41 operands: 42
35	Variable
36	Operation	operator: 43 operands: 44
37	Literal
38	Literal
39	Literal
40	ExprTuple	45, 46
41	Literal
42	ExprTuple	47, 53
43	Literal
44	ExprTuple	57, 58
45	Operation	operator: 49 operands: 48
46	Operation	operator: 49 operands: 50
47	Literal
48	ExprTuple	51, 53
49	Literal
50	ExprTuple	52, 53
51	Operation	operator: 55 operand: 57
52	Operation	operator: 55 operand: 58
53	Literal
54	ExprTuple	57
55	Literal
56	ExprTuple	58
57	Variable
58	Variable

Expression of type Lambda¶

from the theory of proveit.linear_algebra.addition¶

Expression of type Lambda ¶

from the theory of proveit.linear_algebra.addition ¶