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Expression of type ExprTuple

from the theory of proveit.logic.booleans.conjunction

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 Conditional, ExprTuple, Lambda, 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, Forall, InSet
from proveit.numbers import Natural
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([l, m, n], Conditional(Forall(instance_param_or_params = [A_1_to_l, B_1_to_m, C_1_to_n], instance_expr = And(A_1_to_l, B_1_to_m, C_1_to_n), condition = And(A_1_to_l, And(B_1_to_m), C_1_to_n)), And(InSet(l, Natural), InSet(m, Natural), InSet(n, Natural)))))
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(l, m, n\right) \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{l}, B_{1}, B_{2}, \ldots, B_{m}, C_{1}, C_{2}, \ldots, C_{n}~|~A_{1}, A_{2}, \ldots, A_{l}, B_{1} \land  B_{2} \land  \ldots \land  B_{m},C_{1}, C_{2}, \ldots, C_{n}}~\left(A_{1} \land  A_{2} \land  \ldots \land  A_{l}\land B_{1} \land  B_{2} \land  \ldots \land  B_{m}\land C_{1} \land  C_{2} \land  \ldots \land  C_{n}\right) \textrm{ if } l \in \mathbb{N} ,  m \in \mathbb{N} ,  n \in \mathbb{N}\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: 2
body: 3
2ExprTuple27, 38, 31
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 9
5Operationoperator: 28
operands: 8
6Literal
7ExprTuple9
8ExprTuple10, 11, 12
9Lambdaparameters: 21
body: 13
10Operationoperator: 16
operands: 14
11Operationoperator: 16
operands: 15
12Operationoperator: 16
operands: 17
13Conditionalvalue: 18
condition: 19
14ExprTuple27, 20
15ExprTuple38, 20
16Literal
17ExprTuple31, 20
18Operationoperator: 28
operands: 21
19Operationoperator: 28
operands: 22
20Literal
21ExprTuple23, 33, 25
22ExprTuple23, 24, 25
23ExprRangelambda_map: 26
start_index: 37
end_index: 27
24Operationoperator: 28
operands: 29
25ExprRangelambda_map: 30
start_index: 37
end_index: 31
26Lambdaparameter: 43
body: 32
27Variable
28Literal
29ExprTuple33
30Lambdaparameter: 43
body: 34
31Variable
32IndexedVarvariable: 35
index: 43
33ExprRangelambda_map: 36
start_index: 37
end_index: 38
34IndexedVarvariable: 39
index: 43
35Variable
36Lambdaparameter: 43
body: 40
37Literal
38Variable
39Variable
40IndexedVarvariable: 41
index: 43
41Variable
42ExprTuple43
43Variable