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Expression of type Forall

from the theory of proveit.numbers.summation

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 Function, f, n
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Interval, Sum, one, zero
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [n]
expr = Forall(instance_param_or_params = [f], instance_expr = Equals(Sum(index_or_indices = sub_expr1, summand = Function(f, sub_expr1), domain = Interval(zero, one)), Add(Function(f, [zero]), Function(f, [one]))))
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_{f}~\left(\left(\sum_{n = 0}^{1} f\left(n\right)\right) = \left(f\left(0\right) + f\left(1\right)\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: 22
body: 5
4ExprTuple22
5Operationoperator: 6
operands: 7
6Literal
7ExprTuple8, 9
8Operationoperator: 10
operand: 14
9Operationoperator: 12
operands: 13
10Literal
11ExprTuple14
12Literal
13ExprTuple15, 16
14Lambdaparameter: 26
body: 17
15Operationoperator: 22
operand: 30
16Operationoperator: 22
operand: 31
17Conditionalvalue: 20
condition: 21
18ExprTuple30
19ExprTuple31
20Operationoperator: 22
operand: 26
21Operationoperator: 24
operands: 25
22Variable
23ExprTuple26
24Literal
25ExprTuple26, 27
26Variable
27Operationoperator: 28
operands: 29
28Literal
29ExprTuple30, 31
30Literal
31Literal