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Expression of type Forall

from the theory of proveit.numbers.divisibility

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 p, x, y
from proveit.logic import And, Forall, Not
from proveit.numbers import Divides, NaturalPos, greater, one
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [p], instance_expr = Not(And(Divides(p, x), Divides(p, y))), domain = NaturalPos, condition = greater(p, 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_{p \in \mathbb{N}^+~|~p > 1}~(\lnot \left(\left(p \rvert x\right) \land \left(p \rvert y\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: 28
body: 5
4ExprTuple28
5Conditionalvalue: 6
condition: 7
6Operationoperator: 8
operand: 11
7Operationoperator: 14
operands: 10
8Literal
9ExprTuple11
10ExprTuple12, 13
11Operationoperator: 14
operands: 15
12Operationoperator: 16
operands: 17
13Operationoperator: 18
operands: 19
14Literal
15ExprTuple20, 21
16Literal
17ExprTuple28, 22
18Literal
19ExprTuple23, 28
20Operationoperator: 25
operands: 24
21Operationoperator: 25
operands: 26
22Literal
23Literal
24ExprTuple28, 27
25Literal
26ExprTuple28, 29
27Variable
28Variable
29Variable