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, Interval, one, subtract

# build up the expression from sub-expressions
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))

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_{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]

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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 25 body: 4
3	ExprTuple	25
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	25, 12
11	Lambda	parameter: 35 body: 14
12	Operation	operator: 15 operand: 19
13	ExprTuple	35
14	Conditional	value: 17 condition: 18
15	Literal
16	ExprTuple	19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 39 operands: 22
19	Variable
20	Literal
21	ExprTuple	23, 24
22	ExprTuple	35, 25
23	Operation	operator: 26 operand: 30
24	Operation	operator: 28 operands: 29
25	Variable
26	Literal
27	ExprTuple	30
28	Literal
29	ExprTuple	31, 35
30	Lambda	parameter: 43 body: 33
31	Operation	operator: 41 operands: 34
32	ExprTuple	43
33	Conditional	value: 35 condition: 36
34	ExprTuple	37, 38
35	Variable
36	Operation	operator: 39 operands: 40
37	Operation	operator: 41 operands: 42
38	Literal
39	Literal
40	ExprTuple	43, 44
41	Literal
42	ExprTuple	50, 45
43	Variable
44	Operation	operator: 46 operands: 47
45	Operation	operator: 48 operand: 51
46	Literal
47	ExprTuple	51, 50
48	Literal
49	ExprTuple	51
50	Variable
51	Variable