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Expression of type Forall

from the theory of proveit.numbers.multiplication

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 ExprRange, Variable, n, x
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Complex, Mult, Natural, one
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [n, x], instance_expr = Equals(Add(ExprRange(Variable("_a", latex_format = r"{_{-}a}"), x, one, n)), Mult(x, n)), domains = [Natural, Complex])
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_{n \in \mathbb{N}, x \in \mathbb{C}}~\left(\left(x +  x +  ..\left(n - 3\right) \times.. +  x\right) = \left(x \cdot n\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
3Lambdaparameters: 4
body: 5
4ExprTuple28, 30
5Conditionalvalue: 6
condition: 7
6Operationoperator: 8
operands: 9
7Operationoperator: 10
operands: 11
8Literal
9ExprTuple12, 13
10Literal
11ExprTuple14, 15
12Operationoperator: 16
operands: 17
13Operationoperator: 18
operands: 19
14Operationoperator: 21
operands: 20
15Operationoperator: 21
operands: 22
16Literal
17ExprTuple23
18Literal
19ExprTuple30, 28
20ExprTuple28, 24
21Literal
22ExprTuple30, 25
23ExprRangelambda_map: 26
start_index: 27
end_index: 28
24Literal
25Literal
26Lambdaparameter: 31
body: 30
27Literal
28Variable
29ExprTuple31
30Variable
31Variable