Expression of type Forall

from the theory of proveit.numbers.addition.subtraction

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 Add, Complex, Neg, subtract

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

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{C}~|~\left(a + b\right) = c}~\left(\left(-a - b\right) = \left(-c\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	35, 36, 29
5	Conditional	value: 6 condition: 7
6	Operation	operator: 23 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14, 15, 16
11	Operation	operator: 33 operands: 17
12	Operation	operator: 31 operand: 29
13	Operation	operator: 21 operands: 19
14	Operation	operator: 21 operands: 20
15	Operation	operator: 21 operands: 22
16	Operation	operator: 23 operands: 24
17	ExprTuple	25, 26
18	ExprTuple	29
19	ExprTuple	35, 27
20	ExprTuple	36, 27
21	Literal
22	ExprTuple	29, 27
23	Literal
24	ExprTuple	28, 29
25	Operation	operator: 31 operand: 35
26	Operation	operator: 31 operand: 36
27	Literal
28	Operation	operator: 33 operands: 34
29	Variable
30	ExprTuple	35
31	Literal
32	ExprTuple	36
33	Literal
34	ExprTuple	35, 36
35	Variable
36	Variable