Nuprl Lemma : peval_wf
∀[x:formula()]. ∀[v0:{a:formula()| a ⊆ x ∧ (↑pvar?(a))} ⟶ 𝔹]. (peval(v0;x) ∈ 𝔹)
Proof
Definitions occuring in Statement :
peval: peval(v0;x),
psub: a ⊆ b,
pvar?: pvar?(v),
formula: formula(),
assert: ↑b,
bool: 𝔹,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
peval: peval(v0;x),
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
all: ∀x:A. B[x],
uimplies: b supposing a
Lemmas referenced :
valuation-exists-ext,
formula_wf,
psub_wf,
assert_wf,
pvar?_wf,
bool_wf,
psub_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
applyEquality,
thin,
instantiate,
extract_by_obid,
hypothesis,
because_Cache,
sqequalHypSubstitution,
hypothesisEquality,
functionExtensionality,
setEquality,
productEquality,
isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
dependent_set_memberEquality,
dependent_functionElimination,
independent_isectElimination
Latex:
\mforall{}[x:formula()]. \mforall{}[v0:\{a:formula()| a \msubseteq{} x \mwedge{} (\muparrow{}pvar?(a))\} {}\mrightarrow{} \mBbbB{}]. (peval(v0;x) \mmember{} \mBbbB{})
Date html generated:
2018_05_21-PM-08_54_27
Last ObjectModification:
2018_05_19-PM-05_07_05
Theory : general
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