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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_axiom_expr # Load the stored axiom expression as 'stored_expr'
# import the special expression
from proveit.logic.booleans.quantification.universality import forall_in_bool
In [2]:
# check that the built expression is the same as the stored expression
assert forall_in_bool.expr == stored_expr
assert forall_in_bool.expr._style_id == stored_expr._style_id
print("Passed sanity check: forall_in_bool matches stored_expr")
Passed sanity check: forall_in_bool 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}~\left(\left[\forall_{x_{1}, x_{2}, \ldots, x_{n}}~P\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right] \in \mathbb{B}\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: 17
operand: 2
1ExprTuple2
2Lambdaparameter: 26
body: 4
3ExprTuple26
4Conditionalvalue: 5
condition: 6
5Operationoperator: 17
operand: 9
6Operationoperator: 13
operands: 8
7ExprTuple9
8ExprTuple26, 10
9Lambdaparameter: 21
body: 12
10Literal
11ExprTuple21
12Operationoperator: 13
operands: 14
13Literal
14ExprTuple15, 16
15Operationoperator: 17
operand: 19
16Literal
17Literal
18ExprTuple19
19Lambdaparameters: 22
body: 20
20Operationoperator: 21
operands: 22
21Variable
22ExprTuple23
23ExprRangelambda_map: 24
start_index: 25
end_index: 26
24Lambdaparameter: 30
body: 27
25Literal
26Variable
27IndexedVarvariable: 28
index: 30
28Variable
29ExprTuple30
30Variable