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Expression of type Forall

from the theory of proveit.numbers.number_sets.integers

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, b, n
from proveit.logic import Forall
from proveit.numbers import Integer, Interval, LessEq
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b], instance_expr = Forall(instance_param_or_params = [n], instance_expr = LessEq(n, b), domain = Interval(a, b)), 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, b \in \mathbb{Z}}~\left[\forall_{n \in \{a~\ldotp \ldotp~b\}}~\left(n \leq b\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: 6
operand: 2
1ExprTuple2
2Lambdaparameters: 27
body: 3
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 10
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10
8Literal
9ExprTuple11, 12
10Lambdaparameter: 24
body: 14
11Operationoperator: 22
operands: 15
12Operationoperator: 22
operands: 16
13ExprTuple24
14Conditionalvalue: 17
condition: 18
15ExprTuple28, 19
16ExprTuple29, 19
17Operationoperator: 20
operands: 21
18Operationoperator: 22
operands: 23
19Literal
20Literal
21ExprTuple24, 29
22Literal
23ExprTuple24, 25
24Variable
25Operationoperator: 26
operands: 27
26Literal
27ExprTuple28, 29
28Variable
29Variable