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In [1]:
import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.logic.equality import sub_in_right_operands_via_tuple
In [2]:
# check that the built expression is the same as the stored expression
assert sub_in_right_operands_via_tuple.expr == stored_expr
assert sub_in_right_operands_via_tuple.expr._style_id == stored_expr._style_id
print("Passed sanity check: sub_in_right_operands_via_tuple matches stored_expr")
Passed sanity check: sub_in_right_operands_via_tuple matches stored_expr
In [3]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\forall_{n \in \mathbb{N}}~\left[\forall_{P, x_{1}, x_{2}, \ldots, x_{n}, y_{1}, y_{2}, \ldots, y_{n}~|~P\left(x_{1}, x_{2}, \ldots, x_{n}\right), \left(x_{1}, x_{2}, \ldots, x_{n}\right) = \left(y_{1}, y_{2}, \ldots, y_{n}\right)}~P\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right]
In [4]:
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 [5]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 7
operand: 2
1ExprTuple2
2Lambdaparameter: 31
body: 4
3ExprTuple31
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 11
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11
9Literal
10ExprTuple31, 12
11Lambdaparameters: 13
body: 14
12Literal
13ExprTuple21, 26, 27
14Conditionalvalue: 15
condition: 16
15Operationoperator: 21
operands: 25
16Operationoperator: 17
operands: 18
17Literal
18ExprTuple19, 20
19Operationoperator: 21
operands: 24
20Operationoperator: 22
operands: 23
21Variable
22Literal
23ExprTuple24, 25
24ExprTuple26
25ExprTuple27
26ExprRangelambda_map: 28
start_index: 30
end_index: 31
27ExprRangelambda_map: 29
start_index: 30
end_index: 31
28Lambdaparameter: 37
body: 32
29Lambdaparameter: 37
body: 33
30Literal
31Variable
32IndexedVarvariable: 34
index: 37
33IndexedVarvariable: 35
index: 37
34Variable
35Variable
36ExprTuple37
37Variable