Nuprl Lemma : valuation_wf
∀[x:formula()]. ∀[v0:{a:formula()| a ⊆ x ∧ (↑pvar?(a))} ⟶ 𝔹]. ∀[f:{a:formula()| a ⊆ x} ⟶ 𝔹]. (valuation(v0;x;f) ∈ ℙ\000C)
Proof
Definitions occuring in Statement :
valuation: valuation(v0;x;f),
psub: a ⊆ b,
pvar?: pvar?(v),
formula: formula(),
assert: ↑b,
bool: 𝔹,
uall: ∀[x:A]. B[x],
prop: ℙ,
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,
valuation: valuation(v0;x;f),
prop: ℙ,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
and: P ∧ Q,
uimplies: b supposing a,
implies: P ⇒ Q,
cand: A c∧ B,
guard: {T}
Lemmas referenced :
all_wf,
formula_wf,
psub_wf,
equal_wf,
bool_wf,
extend-val_wf,
and_wf,
assert_wf,
pvar?_wf,
set_wf,
subtype_rel_dep_function,
subtype_rel_sets,
psub_transitivity,
subtype_rel_weakening,
ext-eq_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setEquality,
hypothesis,
hypothesisEquality,
lambdaEquality,
lambdaFormation,
setElimination,
rename,
applyEquality,
dependent_set_memberEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
independent_isectElimination,
productElimination,
independent_pairFormation,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[x:formula()]. \mforall{}[v0:\{a:formula()| a \msubseteq{} x \mwedge{} (\muparrow{}pvar?(a))\} {}\mrightarrow{} \mBbbB{}]. \mforall{}[f:\{a:formula()| a \msubseteq{} x\} {}\mrightarrow{} \mBbbB{}].
(valuation(v0;x;f) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-07_15_50
Last ObjectModification:
2015_12_27-AM-11_30_20
Theory : general
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