def nat.lt_not_le
bend-osdev-bpf@0.1.0.0 · PROOF.bend:1940
import bend-osdev-bpf@0.1.0.0/PROOF.bend as PROOF
import Base
1940def nat.lt_not_le(x: Nat, y: Nat, e: {Nat.is_lt(y, x) == True{} : Bool}) -> {Nat.is_le(x, y) == False{} : Bool}:
1941 match x y:
1942 case 0n _:
1943 Empty.absurd({Nat.is_le(0n, y) == False{} : Bool}, absurd.ft(Equal.trans(Bool, False{}, Nat.is_lt(y, 0n), True{}, Equal.sym(Bool, Nat.is_lt(y, 0n), False{}, nat.lt_zero(y)), e)))
1944 case 1n+xp 0n:
1945 {==}
1946 case 1n+xp 1n+yp:
1947 nat.lt_not_le(xp, yp, e)