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Expression of type Forall

from the theory of proveit.logic.booleans.disjunction

In [1]:
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
In [2]:
# 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:
In [3]:
# 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
In [4]:
# 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]
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 7
operand: 2
1ExprTuple2
2Lambdaparameter: 27
body: 4
3ExprTuple27
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 11
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11
9Literal
10ExprTuple27, 12
11Lambdaparameters: 21
body: 13
12Literal
13Conditionalvalue: 14
condition: 15
14Literal
15Operationoperator: 16
operands: 17
16Literal
17ExprTuple18, 19
18Operationoperator: 20
operands: 21
19ExprRangelambda_map: 22
start_index: 26
end_index: 27
20Literal
21ExprTuple23
22Lambdaparameter: 33
body: 24
23ExprRangelambda_map: 25
start_index: 26
end_index: 27
24Operationoperator: 28
operand: 30
25Lambdaparameter: 33
body: 30
26Literal
27Variable
28Literal
29ExprTuple30
30IndexedVarvariable: 31
index: 33
31Variable
32ExprTuple33
33Variable