Expression of type Conditional ¶

from the theory of proveit.numbers.multiplication ¶

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, i, j, x, y
from proveit.core_expr_types import a_1_to_i, b_1_to_j
from proveit.logic import And, Forall, InSet
from proveit.numbers import LessEq, Mult, Natural, RealNonNeg

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [x, y], instance_expr = Forall(instance_param_or_params = [a_1_to_i, b_1_to_j], instance_expr = LessEq(Mult(a_1_to_i, x, b_1_to_j), Mult(a_1_to_i, y, b_1_to_j)), domain = RealNonNeg, condition = LessEq(x, y))), 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_{x, y}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j} \in \mathbb{R}^{\ge 0}~|~x \leq y}~\left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot x\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\right) \leq \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot y\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\right)\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: 11 operand: 5
2	Operation	operator: 20 operands: 4
3	ExprTuple	5
4	ExprTuple	6, 7
5	Lambda	parameters: 33 body: 8
6	Operation	operator: 46 operands: 9
7	Operation	operator: 46 operands: 10
8	Operation	operator: 11 operand: 14
9	ExprTuple	41, 13
10	ExprTuple	44, 13
11	Literal
12	ExprTuple	14
13	Literal
14	Lambda	parameters: 15 body: 16
15	ExprTuple	34, 35
16	Conditional	value: 17 condition: 18
17	Operation	operator: 32 operands: 19
18	Operation	operator: 20 operands: 21
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25, 26
22	Operation	operator: 28 operands: 27
23	Operation	operator: 28 operands: 29
24	ExprRange	lambda_map: 30 start_index: 43 end_index: 41
25	ExprRange	lambda_map: 31 start_index: 43 end_index: 44
26	Operation	operator: 32 operands: 33
27	ExprTuple	34, 38, 35
28	Literal
29	ExprTuple	34, 39, 35
30	Lambda	parameter: 54 body: 36
31	Lambda	parameter: 54 body: 37
32	Literal
33	ExprTuple	38, 39
34	ExprRange	lambda_map: 40 start_index: 43 end_index: 41
35	ExprRange	lambda_map: 42 start_index: 43 end_index: 44
36	Operation	operator: 46 operands: 45
37	Operation	operator: 46 operands: 47
38	Variable
39	Variable
40	Lambda	parameter: 54 body: 48
41	Variable
42	Lambda	parameter: 54 body: 49
43	Literal
44	Variable
45	ExprTuple	48, 50
46	Literal
47	ExprTuple	49, 50
48	IndexedVar	variable: 51 index: 54
49	IndexedVar	variable: 52 index: 54
50	Literal
51	Variable
52	Variable
53	ExprTuple	54
54	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.multiplication¶

Expression of type Conditional ¶

from the theory of proveit.numbers.multiplication ¶