def q_nz_c

bend-collections-laws-math@1.0.0.0 · proofs/math/random/uint64n.bend:50

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend as WI

50def q_nz_c(+q: Nat, +s: Nat, +vn: Nat, +hn: {Nat.is_eq(vn, 0n) == False{} : Bool}, +e: {Nat.add(s, vn) == C.shift(64n, q) : Nat}, +c: Bool, +hc: {Nat.is_eq(q, 0n) == c : Bool}) -> {c == False{} : Bool}:
51  match c:
52    case False{}:
53      {==}
54    case True{}:
55      +hq = N.eq_from_is_eq(q, 0n, hc)
56      +sum0 = Equal.trans(Nat, Nat.add(s, vn), C.shift(64n, q), 0n, e, Equal.trans(Nat, C.shift(64n, q), C.shift(64n, 0n), 0n, Equal.cong(Nat, Nat, z => C.shift(64n, z), q, 0n, hq), WI.shift_zero(64n)))
57      +v0 = add_eq0_r(s, vn, sum0)
58      Empty.absurd({True{} == False{} : Bool}, L.true_false(Equal.trans(Bool, True{}, Nat.is_eq(vn, 0n), False{}, Equal.sym(Bool, Nat.is_eq(vn, 0n), True{}, Equal.cong(Nat, Bool, z => Nat.is_eq(z, 0n), vn, 0n, v0)), hn)))