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Expression of type ExprTuple

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 import A, B, C, Conditional, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, l, m, n
from proveit.core_expr_types import A_1_to_l, B_1_to_m, C_1_to_n
from proveit.logic import And, Boolean, Equals, InSet, Or
from proveit.numbers import one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([A_1_to_l, B_1_to_m, C_1_to_n], Conditional(Equals(Or(A_1_to_l, B_1_to_m, C_1_to_n), Or(A_1_to_l, Or(B_1_to_m), C_1_to_n)).with_wrapping_at(2), And(ExprRange(sub_expr1, InSet(IndexedVar(A, sub_expr1), Boolean), one, l), ExprRange(sub_expr1, InSet(IndexedVar(B, sub_expr1), Boolean), one, m), ExprRange(sub_expr1, InSet(IndexedVar(C, sub_expr1), Boolean), one, 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())
\left(\left(A_{1}, A_{2}, \ldots, A_{l}, B_{1}, B_{2}, \ldots, B_{m}, C_{1}, C_{2}, \ldots, C_{n}\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(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}\right) =  \\ \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) \end{array} \end{array} \textrm{ if } \left(A_{1} \in \mathbb{B}\right) ,  \left(A_{2} \in \mathbb{B}\right) ,  \ldots ,  \left(A_{l} \in \mathbb{B}\right), \left(B_{1} \in \mathbb{B}\right) ,  \left(B_{2} \in \mathbb{B}\right) ,  \ldots ,  \left(B_{m} \in \mathbb{B}\right), \left(C_{1} \in \mathbb{B}\right) ,  \left(C_{2} \in \mathbb{B}\right) ,  \ldots ,  \left(C_{n} \in \mathbb{B}\right)\right..\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameters: 14
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple11, 12, 13
9Operationoperator: 27
operands: 14
10Operationoperator: 27
operands: 15
11ExprRangelambda_map: 16
start_index: 40
end_index: 26
12ExprRangelambda_map: 17
start_index: 40
end_index: 41
13ExprRangelambda_map: 18
start_index: 40
end_index: 30
14ExprTuple19, 35, 21
15ExprTuple19, 20, 21
16Lambdaparameter: 47
body: 22
17Lambdaparameter: 47
body: 23
18Lambdaparameter: 47
body: 24
19ExprRangelambda_map: 25
start_index: 40
end_index: 26
20Operationoperator: 27
operands: 28
21ExprRangelambda_map: 29
start_index: 40
end_index: 30
22Operationoperator: 33
operands: 31
23Operationoperator: 33
operands: 32
24Operationoperator: 33
operands: 34
25Lambdaparameter: 47
body: 36
26Variable
27Literal
28ExprTuple35
29Lambdaparameter: 47
body: 37
30Variable
31ExprTuple36, 38
32ExprTuple44, 38
33Literal
34ExprTuple37, 38
35ExprRangelambda_map: 39
start_index: 40
end_index: 41
36IndexedVarvariable: 42
index: 47
37IndexedVarvariable: 43
index: 47
38Literal
39Lambdaparameter: 47
body: 44
40Literal
41Variable
42Variable
43Variable
44IndexedVarvariable: 45
index: 47
45Variable
46ExprTuple47
47Variable