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