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Expression of type Forall

from the theory of proveit.logic.booleans.conjunction

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, Variable, n
from proveit.logic import And, Forall
from proveit.numbers import one
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A], instance_expr = And(ExprRange(Variable("_a", latex_format = r"{_{-}a}"), A, one, n)), condition = A)
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_{A~|~A}~\left(A \land  A \land  ..\left(n - 3\right) \times.. \land  A\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: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameter: 14
body: 5
4ExprTuple14
5Conditionalvalue: 6
condition: 14
6Operationoperator: 7
operands: 8
7Literal
8ExprTuple9
9ExprRangelambda_map: 10
start_index: 11
end_index: 12
10Lambdaparameter: 15
body: 14
11Literal
12Variable
13ExprTuple15
14Variable
15Variable