lean2/tests/lean/univ.lean
Leonardo de Moura 01259b1e84 feat(kernel): make sure U is the maximal universe
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-29 16:31:00 -08:00

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universe M >= 1
universe U >= M + 1
definition TypeM := (Type M)
universe Z ≥ M+3
(*
local env = get_environment()
assert(env:get_universe_distance("Z", "M") == 3)
assert(not env:get_universe_distance("Z", "U"))
*)
(*
local env = get_environment()
assert(env:get_universe_distance("Z", "M") == 3)
assert(not env:get_universe_distance("Z", "U"))
*)
universe Z1 ≥ M + 1073741824.
universe Z2 ≥ Z1 + 1073741824.
universe U1
universe U2 ≥ U1 + 1
universe U3 ≥ U1 + 1
universe U4 ≥ U2 + 1
universe U4 ≥ U3 + 3
(*
local env = get_environment()
assert(env:get_universe_distance("U4", "U1") == 4)
assert(env:get_universe_distance("U4", "U3") == 3)
assert(env:get_universe_distance("U4", "U2") == 1)
*)
universe U1 ≥ U4.
universe Z >= U.
universe Z >= U + 1.