Expression of type Lambda

from the theory of proveit.logic.equality

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 Lambda, a, c, f, fa, fx, x
from proveit.logic import Equals, Implies

# build up the expression from sub-expressions
expr = Lambda([f, x, a, c], Implies(Equals(x, a), Implies(Equals(fa, c), Equals(fx, c))))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(f, x, a, c\right) \mapsto \left(\left(x = a\right) \Rightarrow \left(\left(f\left(a\right) = c\right) \Rightarrow \left(f\left(x\right) = c\right)\right)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	18, 21, 20, 16
2	Operation	operator: 7 operands: 3
3	ExprTuple	4, 5
4	Operation	operator: 12 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	21, 20
7	Literal
8	ExprTuple	9, 10
9	Operation	operator: 12 operands: 11
10	Operation	operator: 12 operands: 13
11	ExprTuple	14, 16
12	Literal
13	ExprTuple	15, 16
14	Operation	operator: 18 operand: 20
15	Operation	operator: 18 operand: 21
16	Variable
17	ExprTuple	20
18	Variable
19	ExprTuple	21
20	Variable
21	Variable