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Expression of type Lambda

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 B, Conditional, Lambda, l, m, n
from proveit.core_expr_types import A_1_to_l, C_1_to_m, D_1_to_n
from proveit.logic import And, Forall, InSet, Or
from proveit.numbers import Natural
In [2]:
# build up the expression from sub-expressions
expr = Lambda([l, m, n], Conditional(Forall(instance_param_or_params = [A_1_to_l, B, C_1_to_m, D_1_to_n], instance_expr = Or(A_1_to_l, C_1_to_m, B, D_1_to_n), condition = Or(A_1_to_l, B, C_1_to_m, D_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(l, m, n\right) \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{l}, B, C_{1}, C_{2}, \ldots, C_{m}, D_{1}, D_{2}, \ldots, D_{n}~|~A_{1} \lor  A_{2} \lor  \ldots \lor  A_{l} \lor B\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{m}\lor D_{1} \lor  D_{2} \lor  \ldots \lor  D_{n}}~\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{l}\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{m} \lor B\lor D_{1} \lor  D_{2} \lor  \ldots \lor  D_{n}\right) \textrm{ if } l \in \mathbb{N} ,  m \in \mathbb{N} ,  n \in \mathbb{N}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 1
body: 2
1ExprTuple29, 31, 34
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 9
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9
7Literal
8ExprTuple10, 11, 12
9Lambdaparameters: 23
body: 13
10Operationoperator: 16
operands: 14
11Operationoperator: 16
operands: 15
12Operationoperator: 16
operands: 17
13Conditionalvalue: 18
condition: 19
14ExprTuple29, 20
15ExprTuple31, 20
16Literal
17ExprTuple34, 20
18Operationoperator: 22
operands: 21
19Operationoperator: 22
operands: 23
20Literal
21ExprTuple24, 26, 25, 27
22Literal
23ExprTuple24, 25, 26, 27
24ExprRangelambda_map: 28
start_index: 33
end_index: 29
25Variable
26ExprRangelambda_map: 30
start_index: 33
end_index: 31
27ExprRangelambda_map: 32
start_index: 33
end_index: 34
28Lambdaparameter: 42
body: 35
29Variable
30Lambdaparameter: 42
body: 36
31Variable
32Lambdaparameter: 42
body: 37
33Literal
34Variable
35IndexedVarvariable: 38
index: 42
36IndexedVarvariable: 39
index: 42
37IndexedVarvariable: 40
index: 42
38Variable
39Variable
40Variable
41ExprTuple42
42Variable