Expression of type Forall

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, 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 = Forall(instance_param_or_params = [K], instance_expr = 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)))

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())

\forall_{K}~\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()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 24 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 36 body: 3
3	Operation	operator: 24 operand: 5
4	ExprTuple	5
5	Lambda	parameters: 64 body: 6
6	Conditional	value: 7 condition: 8
7	Operation	operator: 24 operand: 12
8	Operation	operator: 10 operands: 11
9	ExprTuple	12
10	Literal
11	ExprTuple	13, 14, 15
12	Lambda	parameter: 42 body: 17
13	Operation	operator: 56 operands: 18
14	Operation	operator: 56 operands: 19
15	Operation	operator: 20 operands: 64
16	ExprTuple	42
17	Conditional	value: 21 condition: 22
18	ExprTuple	68, 23
19	ExprTuple	67, 23
20	Literal
21	Operation	operator: 24 operand: 28
22	Operation	operator: 26 operands: 27
23	Literal
24	Literal
25	ExprTuple	28
26	Literal
27	ExprTuple	42, 29
28	Lambda	parameter: 52 body: 31
29	Operation	operator: 32 operand: 36
30	ExprTuple	52
31	Conditional	value: 34 condition: 35
32	Literal
33	ExprTuple	36
34	Operation	operator: 37 operands: 38
35	Operation	operator: 56 operands: 39
36	Variable
37	Literal
38	ExprTuple	40, 41
39	ExprTuple	52, 42
40	Operation	operator: 43 operand: 47
41	Operation	operator: 45 operands: 46
42	Variable
43	Literal
44	ExprTuple	47
45	Literal
46	ExprTuple	48, 52
47	Lambda	parameter: 60 body: 50
48	Operation	operator: 58 operands: 51
49	ExprTuple	60
50	Conditional	value: 52 condition: 53
51	ExprTuple	54, 55
52	Variable
53	Operation	operator: 56 operands: 57
54	Operation	operator: 58 operands: 59
55	Literal
56	Literal
57	ExprTuple	60, 61
58	Literal
59	ExprTuple	67, 62
60	Variable
61	Operation	operator: 63 operands: 64
62	Operation	operator: 65 operand: 68
63	Literal
64	ExprTuple	68, 67
65	Literal
66	ExprTuple	68
67	Variable
68	Variable