Expression of type Forall¶

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.
# import Expression classes needed to build the expression
from proveit import a, i, va, vi
from proveit.linear_algebra import VecSum
from proveit.logic import Equals, Forall
from proveit.numbers import Integer, Interval

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a], instance_expr = Equals(VecSum(index_or_indices = [i], summand = vi, domain = Interval(a, a)), va), domain = Integer)

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 \in \mathbb{Z}}~\left(\left(\sum_{i=a}^{a} v\left(i\right)\right) = v\left(a\right)\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: 28
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operands: 8
6Operationoperator: 22
operands: 9
7Literal
8ExprTuple10, 11
9ExprTuple28, 12
10Operationoperator: 13
operand: 16
11Operationoperator: 20
operand: 28
12Literal
13Literal
14ExprTuple16
15ExprTuple28
16Lambdaparameter: 24
body: 17
17Conditionalvalue: 18
condition: 19
18Operationoperator: 20
operand: 24
19Operationoperator: 22
operands: 23
20Variable
21ExprTuple24
22Literal
23ExprTuple24, 25
24Variable
25Operationoperator: 26
operands: 27
26Literal
27ExprTuple28, 28
28Variable