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 Equals, Forall, InClass
from proveit.numbers import Add, Interval, one, subtract

# build up the expression from sub-expressions
expr = Conditional(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), InClass(V, VecSpaces(K)))

expr:

# 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 \in V}~\left(\left(\sum_{i=j}^{k} v\right) = \left(\left(\left(k - j\right) + 1\right) \cdot v\right)\right) \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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