Nuprl Lemma : sq_stable__inv_funs
∀[A,B:Type]. ∀[f:A ⟶ B]. ∀[g:B ⟶ A]. SqStable(InvFuns(A;B;f;g))
Proof
Definitions occuring in Statement :
inv_funs: InvFuns(A;B;f;g),
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
inv_funs: InvFuns(A;B;f;g),
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
implies: P ⇒ Q,
sq_stable: SqStable(P),
and: P ∧ Q,
tidentity: Id{T}
Lemmas referenced :
sq_stable__and,
equal_wf,
compose_wf,
tidentity_wf,
sq_stable__equal,
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesisEquality,
hypothesis,
isect_memberEquality,
independent_functionElimination,
lambdaFormation,
because_Cache,
lambdaEquality,
dependent_functionElimination,
productElimination,
independent_pairEquality,
axiomEquality,
productEquality,
Error :functionIsType,
Error :universeIsType,
Error :inhabitedIsType,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[g:B {}\mrightarrow{} A]. SqStable(InvFuns(A;B;f;g))
Date html generated:
2019_06_20-PM-00_26_20
Last ObjectModification:
2018_09_26-PM-00_06_23
Theory : fun_1
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