Expression of type Conditional ¶

from the theory of proveit.numbers.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, b, i, j
from proveit.core_expr_types import a_1_to_i, c_1_to_j
from proveit.logic import And, Forall, InSet
from proveit.numbers import Add, LessEq, Natural, Real, RealNonPos

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_i, c_1_to_j], instance_expr = Forall(instance_param_or_params = [b], instance_expr = LessEq(Add(a_1_to_i, b, c_1_to_j), b), domain = Real), domain = RealNonPos), And(InSet(i, Natural), InSet(j, Natural)))

# 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\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, c_{1}, c_{2}, \ldots, c_{j} \in \mathbb{R}^{\le 0}}~\left[\forall_{b \in \mathbb{R}}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i} + b+ c_{1} +  c_{2} +  \ldots +  c_{j}\right) \leq b\right)\right] \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N}\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: 15 operand: 5
2	Operation	operator: 17 operands: 4
3	ExprTuple	5
4	ExprTuple	6, 7
5	Lambda	parameters: 8 body: 9
6	Operation	operator: 34 operands: 10
7	Operation	operator: 34 operands: 11
8	ExprTuple	41, 43
9	Conditional	value: 12 condition: 13
10	ExprTuple	45, 14
11	ExprTuple	48, 14
12	Operation	operator: 15 operand: 19
13	Operation	operator: 17 operands: 18
14	Literal
15	Literal
16	ExprTuple	19
17	Literal
18	ExprTuple	20, 21
19	Lambda	parameter: 42 body: 23
20	ExprRange	lambda_map: 24 start_index: 47 end_index: 45
21	ExprRange	lambda_map: 25 start_index: 47 end_index: 48
22	ExprTuple	42
23	Conditional	value: 26 condition: 27
24	Lambda	parameter: 54 body: 28
25	Lambda	parameter: 54 body: 29
26	Operation	operator: 30 operands: 31
27	Operation	operator: 34 operands: 32
28	Operation	operator: 34 operands: 33
29	Operation	operator: 34 operands: 35
30	Literal
31	ExprTuple	36, 42
32	ExprTuple	42, 37
33	ExprTuple	49, 38
34	Literal
35	ExprTuple	50, 38
36	Operation	operator: 39 operands: 40
37	Literal
38	Literal
39	Literal
40	ExprTuple	41, 42, 43
41	ExprRange	lambda_map: 44 start_index: 47 end_index: 45
42	Variable
43	ExprRange	lambda_map: 46 start_index: 47 end_index: 48
44	Lambda	parameter: 54 body: 49
45	Variable
46	Lambda	parameter: 54 body: 50
47	Literal
48	Variable
49	IndexedVar	variable: 51 index: 54
50	IndexedVar	variable: 52 index: 54
51	Variable
52	Variable
53	ExprTuple	54
54	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.addition¶

Expression of type Conditional ¶

from the theory of proveit.numbers.addition ¶