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Lifts are isomorphisms

Lax149335.LiftInverses · concepts/Lax149335/LiftInverses.lean · lax-149335

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    Natural Language Statement

    Lemma

    Lemma 7.2. Every lift is an isomorphism, and its inverse is a drop.

    Concept map
    6 concepts
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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

    Each proof establishes this claim relative to its assumptions.

    Lean source view on GitHub

    1import Lax149335.LiftsAndDrops
    2import Lax149335.EquationalTheory
    3
    4/-!
    5---
    6title: Lifts are isomorphisms
    7type: lemma
    8---
    9**Lemma 7.2.** Every lift is an isomorphism, and its inverse is a drop.
    10-/
    11
    12namespace Lax149335.LiftInverses
    13
    14open Lax149335.Types Lax149335.Terms Lax149335.EquationalTheory Lax149335.LiftsAndDrops
    15
    16/-- **Lemma 7.2.** Every lift `f : A → B` has an inverse `g : B → A` that is a drop. -/
    17axiom lift_iso {A B : Ty} (f : Term A B) (hf : IsLift f) :
    18 ∃ g : Term B A, IsDrop g ∧ (f ⨟ g) ≡ₜ Term.id A ∧ (g ⨟ f) ≡ₜ Term.id B
    19
    20end Lax149335.LiftInverses
    21
    Show Proof
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