Nuprl Lemma : inv-rel_wf
∀[A,B:Type]. ∀[f:A ⟶ B]. ∀[finv:B ⟶ (A?)]. (inv-rel(A;B;f;finv) ∈ ℙ)
Proof
Definitions occuring in Statement :
inv-rel: inv-rel(A;B;f;finv),
uall: ∀[x:A]. B[x],
prop: ℙ,
unit: Unit,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
inv-rel: inv-rel(A;B;f;finv),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
and_wf,
all_wf,
equal_wf,
unit_wf2
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
functionEquality,
unionEquality,
hypothesis,
applyEquality,
inlEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[finv:B {}\mrightarrow{} (A?)]. (inv-rel(A;B;f;finv) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-03_54_57
Last ObjectModification:
2015_12_27-PM-01_24_36
Theory : general
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