def
definition
def or abbrev
toLightweight
show as:
view Lean formalization →
formal statement (Lean)
63def toLightweight (R : StrictLogicRealization) : LogicRealization where
64 Carrier := R.Carrier
proof body
Definition body.
65 Cost := R.Cost
66 zeroCost := R.zeroCost
67 compare := R.compare
68 zero := R.one
69 step := fun x => R.compose R.generator x
70 Orbit := FreeOrbit R
71 orbitZero := LogicNat.zero
72 orbitStep := LogicNat.succ
73 interpret := interpret R
74 interpret_zero := rfl
75 interpret_step := by intro n; rfl
76 orbit_no_confusion := by
77 intro n h
78 exact LogicNat.zero_ne_succ n h
79 orbit_step_injective := LogicNat.succ_injective
80 orbit_induction := by
81 intro P h0 hs n
82 exact LogicNat.induction (motive := P) h0 hs n
83 orbitEquivLogicNat := Equiv.refl LogicNat
84 orbitEquiv_zero := rfl
85 orbitEquiv_step := by intro n; rfl
86 identity := R.identity_law
87 nonContradiction := R.non_contradiction_law
88 excludedMiddle := R.excluded_middle_law
89 composition := R.composition_law
90 actionInvariant := R.invariance_law
91 nontrivial := ⟨R.generator, R.nontrivial_law⟩
92
93/-- Strict forced arithmetic is the arithmetic extracted from the derived
94lightweight realization. -/
used by (21)
-
_biology_ok -
_categorical_ok -
_ethics_ok -
_music_ok -
_narrative_ok -
_ordered_ok -
biology_arith_equiv_logicNat -
strictCategorical_arith_equiv_logicNat -
strictBoolean_arith_equiv_logicNat -
ethics_arith_equiv_logicNat -
strict_arith_universal_initial -
strict_metaphysical_ground_unique -
strictUniversalGround -
strictModular_arith_equiv_logicNat -
music_arith_equiv_logicNat -
narrative_arith_equiv_logicNat -
strictOrdered_arith_equiv_logicNat -
positiveRatio_arith_equiv_logicNat -
arith -
arith_equiv_logicNat -
peano_surface