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

# build up the expression from sub-expressions
expr = Lambda(K, Forall(instance_param_or_params = [V], instance_expr = 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)), 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 \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\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)\right]\right]

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Lambda	parameter: 19 body: 1
1	Operation	operator: 8 operand: 3
2	ExprTuple	3
3	Lambda	parameter: 38 body: 5
4	ExprTuple	38
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operand: 12
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12
10	Literal
11	ExprTuple	38, 13
12	Lambda	parameters: 47 body: 14
13	Operation	operator: 15 operand: 19
14	Conditional	value: 17 condition: 18
15	Literal
16	ExprTuple	19
17	Operation	operator: 33 operands: 20
18	Operation	operator: 21 operands: 22
19	Variable
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 26, 27
23	Operation	operator: 58 operand: 35
24	Operation	operator: 52 operands: 29
25	Operation	operator: 31 operands: 30
26	Operation	operator: 31 operands: 32
27	Operation	operator: 33 operands: 34
28	ExprTuple	35
29	ExprTuple	36, 37
30	ExprTuple	60, 38
31	Literal
32	ExprTuple	61, 38
33	Literal
34	ExprTuple	39, 40
35	Operation	operator: 41 operands: 47
36	Operation	operator: 42 operands: 43
37	Operation	operator: 44 operands: 45
38	Variable
39	Operation	operator: 46 operands: 47
40	Literal
41	Literal
42	Literal
43	ExprTuple	48, 49
44	Literal
45	ExprTuple	50, 56
46	Literal
47	ExprTuple	60, 61
48	Operation	operator: 52 operands: 51
49	Operation	operator: 52 operands: 53
50	Literal
51	ExprTuple	54, 56
52	Literal
53	ExprTuple	55, 56
54	Operation	operator: 58 operand: 60
55	Operation	operator: 58 operand: 61
56	Literal
57	ExprTuple	60
58	Literal
59	ExprTuple	61
60	Variable
61	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 ¶