def lt_m
bend-collections-laws-math@1.0.0.0 · proofs/math/typed/fix64.bend:277
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/fix64.bend as Fix64
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/spec/math/generic.bend as SG
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend as WW
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/u64laws.bend as LV
277def lt_m(+mp: Nat, +hp: {C.pow2(64n) == 1n+mp : Nat}, +x: WU.U64) -> {Nat.is_lt(SG.u64_val(x), 1n+mp) == True{} : Bool}:
278 Equal.trans(Bool, Nat.is_lt(SG.u64_val(x), 1n+mp), Nat.is_lt(SG.u64_val(x), C.pow2(64n)), True{}, Equal.cong(Nat, Bool, t => Nat.is_lt(SG.u64_val(x), t), 1n+mp, C.pow2(64n), Equal.sym(Nat, C.pow2(64n), 1n+mp, hp)), WW.lt_of_fits(64n, SG.u64_val(x), LV.vb(x)))