Nuprl Lemma : funinv_wf2
∀[n:ℕ]. ∀[f:{f:ℕn ⟶ ℕn| Inj(ℕn;ℕn;f)} ].  (inv(f) ∈ {f:ℕn ⟶ ℕn| Inj(ℕn;ℕn;f)} )
Proof
Definitions occuring in Statement : 
funinv: inv(f)
, 
inject: Inj(A;B;f)
, 
int_seg: {i..j-}
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
set: {x:A| B[x]} 
, 
function: x:A ⟶ B[x]
, 
natural_number: $n
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
prop: ℙ
, 
nat: ℕ
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
subtype_rel: A ⊆r B
, 
guard: {T}
, 
and: P ∧ Q
, 
int_seg: {i..j-}
, 
all: ∀x:A. B[x]
, 
uimplies: b supposing a
, 
implies: P 
⇒ Q
, 
cand: A c∧ B
Lemmas referenced : 
set_wf, 
int_seg_wf, 
inject_wf, 
nat_wf, 
subtype_rel_sets, 
all_wf, 
equal_wf, 
and_wf, 
funinv_wf, 
surject_wf, 
injection-is-surjection
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalHypSubstitution, 
hypothesis, 
sqequalRule, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
lemma_by_obid, 
isectElimination, 
thin, 
functionEquality, 
natural_numberEquality, 
setElimination, 
rename, 
hypothesisEquality, 
lambdaEquality, 
isect_memberEquality, 
because_Cache, 
applyEquality, 
productEquality, 
intEquality, 
independent_isectElimination, 
setEquality, 
lambdaFormation, 
productElimination, 
dependent_functionElimination
Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[f:\{f:\mBbbN{}n  {}\mrightarrow{}  \mBbbN{}n|  Inj(\mBbbN{}n;\mBbbN{}n;f)\}  ].    (inv(f)  \mmember{}  \{f:\mBbbN{}n  {}\mrightarrow{}  \mBbbN{}n|  Inj(\mBbbN{}n;\mBbbN{}n;f)\}  )
Date html generated:
2016_05_14-AM-07_30_35
Last ObjectModification:
2015_12_26-PM-01_25_52
Theory : int_2
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