Expression of type Lambda ¶

from the theory of proveit.numbers.summation ¶

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 Lambda, a, b, f, fb, fx, x
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Integer, Interval, Less, Sum, one, subtract

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Lambda(f, Forall(instance_param_or_params = [a, b], instance_expr = Equals(Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(a, b)), Add(Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(a, subtract(b, one))), fb)), domain = Integer, condition = Less(a, b)))

# 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())

f \mapsto \left[\forall_{a, b \in \mathbb{Z}~|~a < b}~\left(\left(\sum_{x = a}^{b} f\left(x\right)\right) = \left(\left(\sum_{x = a}^{b - 1} f\left(x\right)\right) + f\left(b\right)\right)\right)\right]

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

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

Expression of type Lambda¶

from the theory of proveit.numbers.summation¶

Expression of type Lambda ¶

from the theory of proveit.numbers.summation ¶