from the theory of proveit.core_expr_types.tuples¶

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.
# import Expression classes needed to build the expression
from proveit import i, j, k
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k, d_1_to_j
from proveit.logic import Equals, Forall
from proveit.numbers import Natural

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [i, j, k], instance_expr = Forall(instance_param_or_params = [a_1_to_i, b_1_to_j, c_1_to_k, d_1_to_j], instance_expr = Equals([a_1_to_i, b_1_to_j, c_1_to_k], [a_1_to_i, d_1_to_j, c_1_to_k]).with_wrapping_at(2), condition = Equals([b_1_to_j], [d_1_to_j])), domain = 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())

\forall_{i, j, k \in \mathbb{N}}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j}, c_{1}, c_{2}, \ldots, c_{k}, d_{1}, d_{2}, \ldots, d_{j}~|~\left(b_{1}, b_{2}, \ldots, b_{j}\right) = \left(d_{1}, d_{2}, \ldots, d_{j}\right)}~\left(\begin{array}{c} \begin{array}{l} \left(a_{1}, a_{2}, \ldots, a_{i},b_{1}, b_{2}, \ldots, b_{j},c_{1}, c_{2}, \ldots, c_{k}\right) =  \\ \left(a_{1}, a_{2}, \ldots, a_{i},d_{1}, d_{2}, \ldots, d_{j},c_{1}, c_{2}, \ldots, c_{k}\right) \end{array} \end{array}\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: 7
operand: 2
1ExprTuple2
2Lambdaparameters: 3
body: 4
3ExprTuple36, 42, 38
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 11
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11
9Literal
10ExprTuple12, 13, 14
11Lambdaparameters: 15
body: 16
12Operationoperator: 19
operands: 17
13Operationoperator: 19
operands: 18
14Operationoperator: 19
operands: 20
15ExprTuple31, 33, 32, 34
16Conditionalvalue: 21
condition: 22
17ExprTuple36, 23
18ExprTuple42, 23
19Literal
20ExprTuple38, 23
21Operationoperator: 25
operands: 24
22Operationoperator: 25
operands: 26
23Literal
24ExprTuple27, 28
25Literal
26ExprTuple29, 30
27ExprTuple31, 33, 32
28ExprTuple31, 34, 32
29ExprTuple33
30ExprTuple34
31ExprRangelambda_map: 35
start_index: 41
end_index: 36
32ExprRangelambda_map: 37
start_index: 41
end_index: 38
33ExprRangelambda_map: 39
start_index: 41
end_index: 42
34ExprRangelambda_map: 40
start_index: 41
end_index: 42
35Lambdaparameter: 52
body: 43
36Variable
37Lambdaparameter: 52
body: 44
38Variable
39Lambdaparameter: 52
body: 45
40Lambdaparameter: 52
body: 46
41Literal
42Variable
43IndexedVarvariable: 47
index: 52
44IndexedVarvariable: 48
index: 52
45IndexedVarvariable: 49
index: 52
46IndexedVarvariable: 50
index: 52
47Variable
48Variable
49Variable
50Variable
51ExprTuple52
52Variable