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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