14 lines
438 B
Text
14 lines
438 B
Text
import standard
|
|
using bool eq_proofs tactic
|
|
|
|
variables a b c : bool
|
|
axiom H1 : a = b
|
|
axiom H2 : b = c
|
|
|
|
check have e1 [fact] : a = b, from H1,
|
|
have e2 : a = c, by apply trans; apply e1; apply H2,
|
|
have e3 : c = a, from e2⁻¹,
|
|
have e4 [fact] : b = a, from e1⁻¹,
|
|
have e5 : b = c, from e4 ⬝ e2,
|
|
have e6 : a = a, from H1 ⬝ H2 ⬝ H2⁻¹ ⬝ H1⁻¹ ⬝ H1 ⬝ H2 ⬝ H2⁻¹ ⬝ H1⁻¹,
|
|
e3 ⬝ e2
|