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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 Q, Qx, f, fx, x
from proveit.logic import Equals, Forall, Implies, InSet
from proveit.numbers import Sum, ZeroSet, zero
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Forall(instance_param_or_params = [f, Q], instance_expr = Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(fx, zero), condition = Qx), InSet(Sum(index_or_indices = sub_expr1, summand = fx, condition = Qx), ZeroSet)))
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, Q}~\left(\left[\forall_{x~|~Q\left(x\right)}~\left(f\left(x\right) = 0\right)\right] \Rightarrow \left(\left[\sum_{x~|~Q\left(x\right)}~f\left(x\right)\right] \in \left\{0\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: 9
operand: 2
1ExprTuple2
2Lambdaparameters: 3
body: 4
3ExprTuple29, 30
4Operationoperator: 5
operands: 6
5Literal
6ExprTuple7, 8
7Operationoperator: 9
operand: 13
8Operationoperator: 11
operands: 12
9Literal
10ExprTuple13
11Literal
12ExprTuple14, 15
13Lambdaparameter: 32
body: 16
14Operationoperator: 17
operand: 22
15Operationoperator: 19
operand: 26
16Conditionalvalue: 21
condition: 28
17Literal
18ExprTuple22
19Literal
20ExprTuple26
21Operationoperator: 23
operands: 24
22Lambdaparameter: 32
body: 25
23Literal
24ExprTuple27, 26
25Conditionalvalue: 27
condition: 28
26Literal
27Operationoperator: 29
operand: 32
28Operationoperator: 30
operand: 32
29Variable
30Variable
31ExprTuple32
32Variable