def inc_val
bend-collections-laws-math@1.0.0.0 · proofs/lib/words32.bend:30
import bend-collections-laws-math@1.0.0.0/proofs/lib/words32.bend as Words32
import Base
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/lib/word.bend as WD
import bend-collections-laws-math@1.0.0.0/proofs/lib/u32div.bend as UD
30def inc_val(+one: Nat, +h1: {one == 1n : Nat}, +i: U32, +h: {Nat.is_lt(1n+UD.v(i), WD.sc(32n, one)) == True{} : Bool}) -> {UD.v(U32.inc(i)) == 1n+UD.v(i) : Nat}:
31 match i:
32 case U32{+w}:
33 +hw = L.subst(Nat, z => {Nat.is_lt(1n+z, WD.sc(32n, one)) == True{} : Bool}, UD.v(U32{w}), WD.uw(32n, w), UD.vw(w), h)
34 Equal.trans(Nat, UD.v(U32{Word.inc(32n, w)}), WD.uw(32n, Word.inc(32n, w)), 1n+UD.v(U32{w}), UD.vw(Word.inc(32n, w)), Equal.trans(Nat, WD.uw(32n, Word.inc(32n, w)), 1n+WD.uw(32n, w), 1n+UD.v(U32{w}), WD.inc_exact(32n, one, h1, w, hw), Equal.cong(Nat, Nat, z => 1n+z, WD.uw(32n, w), UD.v(U32{w}), Equal.sym(Nat, UD.v(U32{w}), WD.uw(32n, w), UD.vw(w)))))