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, b, c, f, fab, fxy, x, y
from proveit.logic import And, Equals, Implies

# build up the expression from sub-expressions
expr = Lambda([f, x, y, a, b, c], Implies(And(Equals(x, a), Equals(y, b)), Implies(Equals(fab, c), Equals(fxy, 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, y, a, b, c\right) \mapsto \left(\left(\left(x = a\right) \land \left(y = b\right)\right) \Rightarrow \left(\left(f\left(a, b\right) = c\right) \Rightarrow \left(f\left(x, y\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	23, 27, 28, 25, 26, 21
2	Operation	operator: 8 operands: 3
3	ExprTuple	4, 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13
10	Operation	operator: 17 operands: 14
11	Operation	operator: 17 operands: 15
12	Operation	operator: 17 operands: 16
13	Operation	operator: 17 operands: 18
14	ExprTuple	27, 25
15	ExprTuple	28, 26
16	ExprTuple	19, 21
17	Literal
18	ExprTuple	20, 21
19	Operation	operator: 23 operands: 22
20	Operation	operator: 23 operands: 24
21	Variable
22	ExprTuple	25, 26
23	Variable
24	ExprTuple	27, 28
25	Variable
26	Variable
27	Variable
28	Variable