Nuprl Lemma : es-E-mk-extended-eo
∀[Info,E:Type]. ∀[dom:E ─→ 𝔹]. ∀[l:E ─→ Id]. ∀[R:E ─→ E ─→ ℙ]. ∀[locless:E ─→ E ─→ 𝔹]. ∀[pred:E ─→ E]. ∀[rank:E ─→ ℕ].
∀[info:E ─→ Info].
∀x:E. ((x ∈ E) ∧ (↑(dom x)))
Proof
Definitions occuring in Statement :
mk-extended-eo: mk-extended-eo,
es-E: E,
Id: Id,
nat: ℕ,
assert: ↑b,
bool: 𝔹,
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
apply: f a,
function: x:A ─→ B[x],
universe: Type
Lemmas :
rec_select_update_lemma,
assert_elim,
subtype_base_sq,
bool_wf,
bool_subtype_base,
set_wf,
assert_wf,
assert_witness,
nat_wf,
Id_wf
Latex:
\mforall{}[Info,E:Type]. \mforall{}[dom:E {}\mrightarrow{} \mBbbB{}]. \mforall{}[l:E {}\mrightarrow{} Id]. \mforall{}[R:E {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}]. \mforall{}[locless:E {}\mrightarrow{} E {}\mrightarrow{} \mBbbB{}].
\mforall{}[pred:E {}\mrightarrow{} E]. \mforall{}[rank:E {}\mrightarrow{} \mBbbN{}]. \mforall{}[info:E {}\mrightarrow{} Info].
\mforall{}x:E. ((x \mmember{} E) \mwedge{} (\muparrow{}(dom x)))
Date html generated:
2015_07_21-PM-04_27_52
Last ObjectModification:
2015_01_27-PM-05_12_56
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