Expression of type Conditional ¶

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

# build up the expression from sub-expressions
expr = Conditional(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)), And(InSet(j, Integer), InSet(k, Integer), 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())

\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] \textrm{ if } j \in \mathbb{Z} ,  k \in \mathbb{Z} ,  j \leq k\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: 18 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	7, 8, 9
6	Lambda	parameter: 36 body: 11
7	Operation	operator: 50 operands: 12
8	Operation	operator: 50 operands: 13
9	Operation	operator: 14 operands: 58
10	ExprTuple	36
11	Conditional	value: 15 condition: 16
12	ExprTuple	62, 17
13	ExprTuple	61, 17
14	Literal
15	Operation	operator: 18 operand: 22
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	22
20	Literal
21	ExprTuple	36, 23
22	Lambda	parameter: 46 body: 25
23	Operation	operator: 26 operand: 30
24	ExprTuple	46
25	Conditional	value: 28 condition: 29
26	Literal
27	ExprTuple	30
28	Operation	operator: 31 operands: 32
29	Operation	operator: 50 operands: 33
30	Variable
31	Literal
32	ExprTuple	34, 35
33	ExprTuple	46, 36
34	Operation	operator: 37 operand: 41
35	Operation	operator: 39 operands: 40
36	Variable
37	Literal
38	ExprTuple	41
39	Literal
40	ExprTuple	42, 46
41	Lambda	parameter: 54 body: 44
42	Operation	operator: 52 operands: 45
43	ExprTuple	54
44	Conditional	value: 46 condition: 47
45	ExprTuple	48, 49
46	Variable
47	Operation	operator: 50 operands: 51
48	Operation	operator: 52 operands: 53
49	Literal
50	Literal
51	ExprTuple	54, 55
52	Literal
53	ExprTuple	61, 56
54	Variable
55	Operation	operator: 57 operands: 58
56	Operation	operator: 59 operand: 62
57	Literal
58	ExprTuple	62, 61
59	Literal
60	ExprTuple	62
61	Variable
62	Variable

Expression of type Conditional¶

from the theory of proveit.linear_algebra.addition¶

Expression of type Conditional ¶

from the theory of proveit.linear_algebra.addition ¶