Expression of type Forall

from the theory of proveit.numbers.absolute_value

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
from proveit.logic import Equals, Forall
from proveit.numbers import Abs, Complex, subtract

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b], instance_expr = Equals(Abs(subtract(a, b)), Abs(subtract(b, a))), domain = Complex)

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 \in \mathbb{C}}~\left(\left|a - b\right| = \left|b - a\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	34, 33
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
12	Operation	operator: 17 operand: 22
13	Operation	operator: 17 operand: 23
14	Operation	operator: 20 operands: 19
15	Operation	operator: 20 operands: 21
16	ExprTuple	22
17	Literal
18	ExprTuple	23
19	ExprTuple	34, 24
20	Literal
21	ExprTuple	33, 24
22	Operation	operator: 26 operands: 25
23	Operation	operator: 26 operands: 27
24	Literal
25	ExprTuple	34, 28
26	Literal
27	ExprTuple	33, 29
28	Operation	operator: 31 operand: 33
29	Operation	operator: 31 operand: 34
30	ExprTuple	33
31	Literal
32	ExprTuple	34
33	Variable
34	Variable