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Expression of type Forall

from the theory of proveit.logic.booleans.disjunction

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.core_expr_types import A_1_to_l, B_1_to_m, C_1_to_n
from proveit.logic import Forall, Or
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A_1_to_l, B_1_to_m, C_1_to_n], instance_expr = Or(A_1_to_l, Or(B_1_to_m), C_1_to_n), condition = Or(A_1_to_l, B_1_to_m, C_1_to_n))
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_{l}, B_{1}, B_{2}, \ldots, B_{m}, C_{1}, C_{2}, \ldots, C_{n}~|~A_{1} \lor  A_{2} \lor  \ldots \lor  A_{l}\lor B_{1} \lor  B_{2} \lor  \ldots \lor  B_{m}\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{n}}~\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{l} \lor \left(B_{1} \lor  B_{2} \lor  \ldots \lor  B_{m}\right)\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{n}\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: 8
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 12
operands: 7
6Operationoperator: 12
operands: 8
7ExprTuple10, 9, 11
8ExprTuple10, 18, 11
9Operationoperator: 12
operands: 13
10ExprRangelambda_map: 14
start_index: 22
end_index: 15
11ExprRangelambda_map: 16
start_index: 22
end_index: 17
12Literal
13ExprTuple18
14Lambdaparameter: 29
body: 19
15Variable
16Lambdaparameter: 29
body: 20
17Variable
18ExprRangelambda_map: 21
start_index: 22
end_index: 23
19IndexedVarvariable: 24
index: 29
20IndexedVarvariable: 25
index: 29
21Lambdaparameter: 29
body: 26
22Literal
23Variable
24Variable
25Variable
26IndexedVarvariable: 27
index: 29
27Variable
28ExprTuple29
29Variable