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Axiom substitution of type Forall

from the theory of proveit.logic.equality

see dependencies

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.equality import substitution
In [2]:
# check that the built expression is the same as the stored expression
assert substitution.expr == stored_expr
assert substitution.expr._style_id == stored_expr._style_id
print("Passed sanity check: substitution matches stored_expr")
Passed sanity check: substitution matches stored_expr
In [3]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\forall_{f, x, y~|~x = y}~\left(f\left(x\right) = f\left(y\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: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 4
body: 5
4ExprTuple14, 16, 17
5Conditionalvalue: 6
condition: 7
6Operationoperator: 9
operands: 8
7Operationoperator: 9
operands: 10
8ExprTuple11, 12
9Literal
10ExprTuple16, 17
11Operationoperator: 14
operand: 16
12Operationoperator: 14
operand: 17
13ExprTuple16
14Variable
15ExprTuple17
16Variable
17Variable