Expression of type Conditional ¶

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 Conditional, Function, f, g, k, l, m, n
from proveit.logic import And, Equals, Forall, Implies, InSet
from proveit.numbers import Integer, Interval, Sum

# build up the expression from sub-expressions
sub_expr1 = [k]
sub_expr2 = [l]
sub_expr3 = Interval(m, n)
expr = Conditional(Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Function(f, sub_expr1), Function(g, sub_expr1)), domain = sub_expr3), Equals(Sum(index_or_indices = sub_expr2, summand = Function(f, sub_expr2), domain = sub_expr3), Sum(index_or_indices = sub_expr2, summand = Function(g, sub_expr2), domain = sub_expr3))), And(InSet(m, Integer), InSet(n, Integer)))

# 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\{\left[\forall_{k \in \{m~\ldotp \ldotp~n\}}~\left(f\left(k\right) = g\left(k\right)\right)\right] \Rightarrow \left(\left(\sum_{l = m}^{n} f\left(l\right)\right) = \left(\sum_{l = m}^{n} g\left(l\right)\right)\right) \textrm{ if } m \in \mathbb{Z} ,  n \in \mathbb{Z}\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

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

Expression of type Conditional¶

from the theory of proveit.numbers.summation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.summation ¶