Expression of type Forall

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 x, y
from proveit.core_expr_types import a_1_to_i, b_1_to_j
from proveit.logic import Forall
from proveit.numbers import Less, Mult, RealPos

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a_1_to_i, b_1_to_j], instance_expr = Less(Mult(a_1_to_i, x, b_1_to_j), Mult(a_1_to_i, y, b_1_to_j)), domain = RealPos, condition = Less(x, y))

expr:

# 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())

\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j} \in \mathbb{R}^+~|~x < 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) < \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)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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