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 a, b
from proveit.logic import Equals, Forall, InSet, Or
from proveit.numbers import Complex, Mult, ZeroSet, zero

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b], instance_expr = InSet(Mult(a, b), ZeroSet), domain = Complex, condition = Or(Equals(a, zero), Equals(b, zero)))

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(a = 0\right) \lor \left(b = 0\right)}~\left(\left(a \cdot b\right) \in \left\{0\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: 16 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 20 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13, 14
10	Operation	operator: 15 operands: 16
11	Operation	operator: 17 operand: 32
12	Operation	operator: 20 operands: 19
13	Operation	operator: 20 operands: 21
14	Operation	operator: 22 operands: 23
15	Literal
16	ExprTuple	30, 31
17	Literal
18	ExprTuple	32
19	ExprTuple	30, 24
20	Literal
21	ExprTuple	31, 24
22	Literal
23	ExprTuple	25, 26
24	Literal
25	Operation	operator: 28 operands: 27
26	Operation	operator: 28 operands: 29
27	ExprTuple	30, 32
28	Literal
29	ExprTuple	31, 32
30	Variable
31	Variable
32	Literal