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Expression of type Forall

from the theory of proveit.logic.sets.enumeration

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 b
from proveit.core_expr_types import a_1_to_i, c_1_to_j, d_1_to_k
from proveit.logic import Equals, Forall, Set
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a_1_to_i, b, c_1_to_j, d_1_to_k], instance_expr = Equals(Set(a_1_to_i, b, c_1_to_j, d_1_to_k), Set(a_1_to_i, c_1_to_j, b, d_1_to_k)))
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_{1}, a_{2}, \ldots, a_{i}, b, c_{1}, c_{2}, \ldots, c_{j}, d_{1}, d_{2}, \ldots, d_{k}}~\left(\left\{a_{1}, a_{2}, \ldots, a_{i}, b,c_{1}, c_{2}, \ldots, c_{j},d_{1}, d_{2}, \ldots, d_{k}\right\} = \left\{a_{1}, a_{2}, \ldots, a_{i},c_{1}, c_{2}, \ldots, c_{j}, b,d_{1}, d_{2}, \ldots, d_{k}\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: 9
body: 4
4Operationoperator: 5
operands: 6
5Literal
6ExprTuple7, 8
7Operationoperator: 10
operands: 9
8Operationoperator: 10
operands: 11
9ExprTuple12, 14, 13, 15
10Literal
11ExprTuple12, 13, 14, 15
12ExprRangelambda_map: 16
start_index: 21
end_index: 17
13ExprRangelambda_map: 18
start_index: 21
end_index: 19
14Variable
15ExprRangelambda_map: 20
start_index: 21
end_index: 22
16Lambdaparameter: 30
body: 23
17Variable
18Lambdaparameter: 30
body: 24
19Variable
20Lambdaparameter: 30
body: 25
21Literal
22Variable
23IndexedVarvariable: 26
index: 30
24IndexedVarvariable: 27
index: 30
25IndexedVarvariable: 28
index: 30
26Variable
27Variable
28Variable
29ExprTuple30
30Variable