Plain-language statement
Note that we cannot prove the reverse implication because all of our hypotheses at this stage are about permutations, not objects.
Exact Lean statement
theorem card_tSet_le (β : TypeIndex) [LeLevel β] :
#(TSet β) ≤ #μFormal artifact
Lean source
theorem card_tSet_le (β : TypeIndex) [LeLevel β] : #(TSet β) ≤ #μ := by refine (mk_le_of_injective (f := λ x : TSet β ↦ (Tangle.code ⟨x, (exists_support x).choose, (exists_support x).choose_spec⟩, (exists_support x).choose)) ?_).trans ?_ · intro x y h rw [Prod.mk.injEq, Tangle.code_eq_code_iff] at h obtain ⟨⟨ρ, hρ⟩, h⟩ := h have := (exists_support x).choose_spec.supports ρ ?_ · have hρx := congr_arg (·.set) hρ simp only [Tangle.smul_set] at hρx rw [← hρx, this] · have hρx := congr_arg (·.support) hρ simp only [Tangle.smul_support] at hρx rw [hρx, h] · rw [mk_prod, Cardinal.lift_id, Cardinal.lift_id] apply mul_le_of_le μ_isStrongLimit.aleph0_le (card_codingFunction β).le rw [card_support]- Project
- Con(NF)
- License
- Apache-2.0
- Commit
- 55b939a3acf9
- Source
- ConNF/Counting/Conclusions.lean:62-80
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Related declarations
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Project documentation
The main lemma about how approximations interact with actions.
Source project: Con(NF)
Person-level attribution pending.
Smul interference
ConNF.BasePerm.smul_interference
Plain-language statement
Base permutations commute with the interference of near-litters.
Source project: Con(NF)
Person-level attribution pending.
Str Action flex Approx coherent
ConNF.StrAction.flexApprox_coherent
Plain-language statement
TODO: Put this in the blueprint.
Source project: Con(NF)
Person-level attribution pending.