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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 And, Forall, InSet
from proveit.numbers import Integer, Interval, LessEq
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b, n], instance_expr = InSet(n, Interval(a, b)), domain = Integer, condition = And(LessEq(a, n), LessEq(n, b)).with_total_ordering_style())
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, n \in \mathbb{Z}~|~a \leq n \leq b}~\left(n \in \{a~\ldotp \ldotp~b\}\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
4ExprTuple29, 31, 30
5Conditionalvalue: 6
condition: 7
6Operationoperator: 19
operands: 8
7Operationoperator: 21
operands: 9
8ExprTuple30, 10
9ExprTuple11, 12, 13, 14
10Operationoperator: 15
operands: 16
11Operationoperator: 19
operands: 17
12Operationoperator: 19
operands: 18
13Operationoperator: 19
operands: 20
14Operationoperator: 21
operands: 22
15Literal
16ExprTuple29, 31
17ExprTuple29, 23
18ExprTuple31, 23
19Literal
20ExprTuple30, 23
21Literal
22ExprTuple24, 25
23Literal
24Operationoperator: 27
operands: 26
25Operationoperator: 27
operands: 28
26ExprTuple29, 30
27Literal
28ExprTuple30, 31
29Variable
30Variable
31Variable