Expression of type Forall

from the theory of proveit.numbers.modular

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 a, b, c
from proveit.logic import Equals, Forall
from proveit.numbers import ModAbs, Mult, Real

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b, c], instance_expr = Equals(Mult(a, ModAbs(b, c)), ModAbs(Mult(a, b), Mult(a, c))), domain = Real)

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, b, c \in \mathbb{R}}~\left(\left(a \cdot \left|b\right|_{\textup{mod}\thinspace c}\right) = \left|a \cdot b\right|_{\textup{mod}\thinspace a \cdot c}\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	33, 32, 34
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15, 16
12	Operation	operator: 30 operands: 17
13	Operation	operator: 27 operands: 18
14	Operation	operator: 21 operands: 19
15	Operation	operator: 21 operands: 20
16	Operation	operator: 21 operands: 22
17	ExprTuple	33, 23
18	ExprTuple	24, 25
19	ExprTuple	33, 26
20	ExprTuple	32, 26
21	Literal
22	ExprTuple	34, 26
23	Operation	operator: 27 operands: 28
24	Operation	operator: 30 operands: 29
25	Operation	operator: 30 operands: 31
26	Literal
27	Literal
28	ExprTuple	32, 34
29	ExprTuple	33, 32
30	Literal
31	ExprTuple	33, 34
32	Variable
33	Variable
34	Variable