from the theory of proveit.core_expr_types.conditionals¶

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 Conditional, ExprTuple, Lambda, a
from proveit.core_expr_types import Q_1_to_m, R_1_to_n
from proveit.logic import And, Equals, TRUE

In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, Q_1_to_m, R_1_to_n], Equals(Conditional(a, And(Q_1_to_m, TRUE, R_1_to_n)), Conditional(a, And(Q_1_to_m, R_1_to_n))).with_wrapping_at(1)))

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, Q_{1}, Q_{2}, \ldots, Q_{m}, R_{1}, R_{2}, \ldots, R_{n}\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \left\{a \textrm{ if } Q_{1} ,  Q_{2} ,  \ldots ,  Q_{m} ,  \top, R_{1} ,  R_{2} ,  \ldots ,  R_{n}\right.. \\  = \left\{a \textrm{ if } Q_{1} ,  Q_{2} ,  \ldots ,  Q_{m}, R_{1} ,  R_{2} ,  \ldots ,  R_{n}\right.. \end{array} \end{array}\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
2ExprTuple9, 15, 16
3Operationoperator: 4
operands: 5
4Literal
5ExprTuple6, 7
6Conditionalvalue: 9
condition: 8
7Conditionalvalue: 9
condition: 10
8Operationoperator: 12
operands: 11
9Variable
10Operationoperator: 12
operands: 13
11ExprTuple15, 14, 16
12Literal
13ExprTuple15, 16
14Literal
15ExprRangelambda_map: 17
start_index: 20
end_index: 18
16ExprRangelambda_map: 19
start_index: 20
end_index: 21
17Lambdaparameter: 27
body: 22
18Variable
19Lambdaparameter: 27
body: 23
20Literal
21Variable
22IndexedVarvariable: 24
index: 27
23IndexedVarvariable: 25
index: 27
24Variable
25Variable
26ExprTuple27
27Variable