Expression of type Forall

from the theory of proveit.logic.booleans.disjunction

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, ExprRange, IndexedVar, Variable, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import FALSE, Forall, Not, Or
from proveit.numbers import Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Forall(instance_param_or_params = [m], instance_expr = Forall(instance_param_or_params = [A_1_to_m], instance_expr = FALSE, conditions = [Or(A_1_to_m), ExprRange(sub_expr1, Not(IndexedVar(A, sub_expr1)), one, m)]), domain = Natural)

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_{m \in \mathbb{N}}~\left[\forall_{A_{1}, A_{2}, \ldots, A_{m}~|~A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m},(\lnot A_{1}), (\lnot A_{2}), \ldots, (\lnot A_{m})}~\bot\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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 27 body: 4
3	ExprTuple	27
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	27, 12
11	Lambda	parameters: 21 body: 13
12	Literal
13	Conditional	value: 14 condition: 15
14	Literal
15	Operation	operator: 16 operands: 17
16	Literal
17	ExprTuple	18, 19
18	Operation	operator: 20 operands: 21
19	ExprRange	lambda_map: 22 start_index: 26 end_index: 27
20	Literal
21	ExprTuple	23
22	Lambda	parameter: 33 body: 24
23	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
24	Operation	operator: 28 operand: 30
25	Lambda	parameter: 33 body: 30
26	Literal
27	Variable
28	Literal
29	ExprTuple	30
30	IndexedVar	variable: 31 index: 33
31	Variable
32	ExprTuple	33
33	Variable