Nuprl Lemma : inv_funs_sym
∀[A,B:Type]. ∀[f:A ⟶ B]. ∀[g:B ⟶ A]. InvFuns(B;A;g;f) supposing InvFuns(A;B;f;g)
Proof
Definitions occuring in Statement :
inv_funs: InvFuns(A;B;f;g),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
inv_funs: InvFuns(A;B;f;g),
and: P ∧ Q,
cand: A c∧ B,
prop: ℙ
Lemmas referenced :
inv_funs_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
independent_pairFormation,
sqequalRule,
independent_pairEquality,
axiomEquality,
Error :universeIsType,
extract_by_obid,
isectElimination,
hypothesisEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
Error :functionIsType,
because_Cache,
functionEquality,
Error :inhabitedIsType,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[g:B {}\mrightarrow{} A]. InvFuns(B;A;g;f) supposing InvFuns(A;B;f;g)
Date html generated:
2019_06_20-PM-00_26_30
Last ObjectModification:
2018_09_26-PM-00_09_28
Theory : fun_1
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