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, i, j, k, v
from proveit.linear_algebra import ScalarMult, VecSpaces, VecSum
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Integer, Interval, LessEq, one, subtract

# build up the expression from sub-expressions
expr = Lambda(K, Forall(instance_param_or_params = [j, k], instance_expr = Forall(instance_param_or_params = [V], instance_expr = Forall(instance_param_or_params = [v], instance_expr = Equals(VecSum(index_or_indices = [i], summand = v, domain = Interval(j, k)), ScalarMult(Add(subtract(k, j), one), v)), domain = V), domain = VecSpaces(K)), domain = Integer, condition = LessEq(j, 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_{j, k \in \mathbb{Z}~|~j \leq k}~\left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{v \in V}~\left(\left(\sum_{i=j}^{k} v\right) = \left(\left(\left(k - j\right) + 1\right) \cdot v\right)\right)\right]\right]\right]

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Lambda	parameter: 34 body: 1
1	Operation	operator: 22 operand: 3
2	ExprTuple	3
3	Lambda	parameters: 62 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 22 operand: 10
6	Operation	operator: 8 operands: 9
7	ExprTuple	10
8	Literal
9	ExprTuple	11, 12, 13
10	Lambda	parameter: 40 body: 15
11	Operation	operator: 54 operands: 16
12	Operation	operator: 54 operands: 17
13	Operation	operator: 18 operands: 62
14	ExprTuple	40
15	Conditional	value: 19 condition: 20
16	ExprTuple	66, 21
17	ExprTuple	65, 21
18	Literal
19	Operation	operator: 22 operand: 26
20	Operation	operator: 24 operands: 25
21	Literal
22	Literal
23	ExprTuple	26
24	Literal
25	ExprTuple	40, 27
26	Lambda	parameter: 50 body: 29
27	Operation	operator: 30 operand: 34
28	ExprTuple	50
29	Conditional	value: 32 condition: 33
30	Literal
31	ExprTuple	34
32	Operation	operator: 35 operands: 36
33	Operation	operator: 54 operands: 37
34	Variable
35	Literal
36	ExprTuple	38, 39
37	ExprTuple	50, 40
38	Operation	operator: 41 operand: 45
39	Operation	operator: 43 operands: 44
40	Variable
41	Literal
42	ExprTuple	45
43	Literal
44	ExprTuple	46, 50
45	Lambda	parameter: 58 body: 48
46	Operation	operator: 56 operands: 49
47	ExprTuple	58
48	Conditional	value: 50 condition: 51
49	ExprTuple	52, 53
50	Variable
51	Operation	operator: 54 operands: 55
52	Operation	operator: 56 operands: 57
53	Literal
54	Literal
55	ExprTuple	58, 59
56	Literal
57	ExprTuple	65, 60
58	Variable
59	Operation	operator: 61 operands: 62
60	Operation	operator: 63 operand: 66
61	Literal
62	ExprTuple	66, 65
63	Literal
64	ExprTuple	66
65	Variable
66	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 ¶