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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