Nuprl Lemma : inv_funs_wf
∀[A,B:Type]. ∀[f:A ⟶ B]. ∀[g:B ⟶ A]. (InvFuns(A;B;f;g) ∈ ℙ)
Proof
Definitions occuring in Statement :
inv_funs: InvFuns(A;B;f;g),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
inv_funs: InvFuns(A;B;f;g),
prop: ℙ,
and: P ∧ Q,
tidentity: Id{T}
Lemmas referenced :
equal_wf,
compose_wf,
tidentity_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :functionIsType,
Error :universeIsType,
isect_memberEquality,
because_Cache,
Error :inhabitedIsType,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[g:B {}\mrightarrow{} A]. (InvFuns(A;B;f;g) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-00_26_19
Last ObjectModification:
2018_09_26-AM-11_49_29
Theory : fun_1
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