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 ExprRange, IndexedVar, Variable, a, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Equals, Forall, InSet, Or
from proveit.numbers import Complex, Mult, ZeroSet, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Forall(instance_param_or_params = [a_1_to_n], instance_expr = InSet(Mult(a_1_to_n), ZeroSet), domain = Complex, condition = Or(ExprRange(sub_expr1, Equals(IndexedVar(a, sub_expr1), zero), one, n)))

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_{n} \in \mathbb{C}~|~\left(a_{1} = 0\right) \lor  \left(a_{2} = 0\right) \lor  \ldots \lor  \left(a_{n} = 0\right)}~\left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{n}\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: 15 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 25 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13
10	Operation	operator: 14 operands: 15
11	Operation	operator: 16 operand: 35
12	ExprRange	lambda_map: 18 start_index: 28 end_index: 29
13	Operation	operator: 19 operands: 20
14	Literal
15	ExprTuple	21
16	Literal
17	ExprTuple	35
18	Lambda	parameter: 38 body: 22
19	Literal
20	ExprTuple	23
21	ExprRange	lambda_map: 24 start_index: 28 end_index: 29
22	Operation	operator: 25 operands: 26
23	ExprRange	lambda_map: 27 start_index: 28 end_index: 29
24	Lambda	parameter: 38 body: 34
25	Literal
26	ExprTuple	34, 30
27	Lambda	parameter: 38 body: 31
28	Literal
29	Variable
30	Literal
31	Operation	operator: 32 operands: 33
32	Literal
33	ExprTuple	34, 35
34	IndexedVar	variable: 36 index: 38
35	Literal
36	Variable
37	ExprTuple	38
38	Variable