### Nuprl Lemma : inverse_wf

`∀[T:Type]. ∀[op:T ⟶ T ⟶ T]. ∀[id:T]. ∀[inv:T ⟶ T].  (Inverse(T;op;id;inv) ∈ ℙ)`

Proof

Definitions occuring in Statement :  inverse: `Inverse(T;op;id;inv)` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  inverse: `Inverse(T;op;id;inv)` uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` infix_ap: `x f y` so_apply: `x[s]`
Lemmas referenced :  uall_wf and_wf equal_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality applyEquality hypothesis axiomEquality equalityTransitivity equalitySymmetry functionEquality isect_memberEquality because_Cache universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[op:T  {}\mrightarrow{}  T  {}\mrightarrow{}  T].  \mforall{}[id:T].  \mforall{}[inv:T  {}\mrightarrow{}  T].    (Inverse(T;op;id;inv)  \mmember{}  \mBbbP{})

Date html generated: 2016_05_13-PM-04_08_58
Last ObjectModification: 2015_12_26-AM-11_03_11

Theory : fun_1

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