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Expression of type Forall

from the theory of proveit.logic.sets.subtraction

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 S, x, y
from proveit.logic import And, Difference, Forall, InSet, NotEquals, Set
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [S, y], instance_expr = Forall(instance_param_or_params = [x], instance_expr = And(InSet(x, S), NotEquals(x, y)), domain = Difference(S, Set(y))))
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_{S, y}~\left[\forall_{x \in S - \left\{y\right\}}~\left(\left(x \in S\right) \land \left(x \neq y\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: 5
operand: 2
1ExprTuple2
2Lambdaparameters: 3
body: 4
3ExprTuple25, 29
4Operationoperator: 5
operand: 7
5Literal
6ExprTuple7
7Lambdaparameter: 24
body: 9
8ExprTuple24
9Conditionalvalue: 10
condition: 11
10Operationoperator: 12
operands: 13
11Operationoperator: 18
operands: 14
12Literal
13ExprTuple15, 16
14ExprTuple24, 17
15Operationoperator: 18
operands: 19
16Operationoperator: 20
operands: 21
17Operationoperator: 22
operands: 23
18Literal
19ExprTuple24, 25
20Literal
21ExprTuple24, 29
22Literal
23ExprTuple25, 26
24Variable
25Variable
26Operationoperator: 27
operand: 29
27Literal
28ExprTuple29
29Variable