lean2/tests/lean/have1.lean
Leonardo de Moura 68d9bef860 refactor(library): add 'eq' and 'ne' namespaces
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-09-04 18:41:06 -07:00

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import logic
open bool eq_ops tactic eq
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