Nuprl Lemma : language1_wf
∀[fml:D:Type ⟶ ℙ ⟶ (D ⟶ ℙ) ⟶ (D ⟶ ℙ) ⟶ (D ⟶ D ⟶ ℙ) ⟶ (D ⟶ D ⟶ ℙ) ⟶ (D ⟶ D ⟶ ℙ) ⟶ (D ⟶ D ⟶ D ⟶ ℙ) ⟶ ℙ]
  (language1{i:l}(D,A,B,C,P,Q,R,H.fml[D;A;B;C;P;Q;R;H]) ∈ ℙ')
Proof
Definitions occuring in Statement : 
language1: language1{i:l}(D,A,B,C,P,Q,R,H.fml[D;A;B;C;P;Q;R;H])
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
so_apply: x[a;b;c;d;e;f;g;h]
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
language1: language1{i:l}(D,A,B,C,P,Q,R,H.fml[D;A;B;C;P;Q;R;H])
, 
so_lambda: λ2x.t[x]
, 
prop: ℙ
, 
so_apply: x[a;b;c;d;e;f;g;h]
, 
subtype_rel: A ⊆r B
, 
so_apply: x[s]
Lemmas referenced : 
uall_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
thin, 
instantiate, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
universeEquality, 
lambdaEquality, 
functionEquality, 
cumulativity, 
hypothesisEquality, 
because_Cache, 
applyEquality, 
hypothesis, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry
Latex:
\mforall{}[fml:D:Type
            {}\mrightarrow{}  \mBbbP{}
            {}\mrightarrow{}  (D  {}\mrightarrow{}  \mBbbP{})
            {}\mrightarrow{}  (D  {}\mrightarrow{}  \mBbbP{})
            {}\mrightarrow{}  (D  {}\mrightarrow{}  D  {}\mrightarrow{}  \mBbbP{})
            {}\mrightarrow{}  (D  {}\mrightarrow{}  D  {}\mrightarrow{}  \mBbbP{})
            {}\mrightarrow{}  (D  {}\mrightarrow{}  D  {}\mrightarrow{}  \mBbbP{})
            {}\mrightarrow{}  (D  {}\mrightarrow{}  D  {}\mrightarrow{}  D  {}\mrightarrow{}  \mBbbP{})
            {}\mrightarrow{}  \mBbbP{}]
    (language1\{i:l\}(D,A,B,C,P,Q,R,H.fml[D;A;B;C;P;Q;R;H])  \mmember{}  \mBbbP{}')
Date html generated:
2016_05_16-AM-09_07_37
Last ObjectModification:
2015_12_28-PM-07_03_26
Theory : first-order!and!ancestral!logic
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