Nuprl Lemma : valuation-val
∀[z:formula()]. ∀[v0:{a:formula()| a ⊆ z ∧ (↑pvar?(a))} ⟶ 𝔹]. ∀[f:{f:{a:formula()| a ⊆ z} ⟶ 𝔹| valuation(v0;z;f)} ].
f z = extend-val(v0;f;z)
Proof
Definitions occuring in Statement :
valuation: valuation(v0;x;f),
extend-val: extend-val(v0;g;x),
psub: a ⊆ b,
pvar?: pvar?(v),
formula: formula(),
assert: ↑b,
bool: 𝔹,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
valuation: valuation(v0;x;f),
all: ∀x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
and: P ∧ Q,
uimplies: b supposing a
Lemmas referenced :
psub_wf,
set_wf,
formula_wf,
bool_wf,
valuation_wf,
and_wf,
assert_wf,
pvar?_wf,
psub_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
setElimination,
thin,
rename,
sqequalHypSubstitution,
hypothesis,
dependent_functionElimination,
dependent_set_memberEquality,
hypothesisEquality,
lemma_by_obid,
isectElimination,
functionEquality,
setEquality,
sqequalRule,
lambdaEquality,
isect_memberEquality,
axiomEquality,
because_Cache,
independent_isectElimination
Latex:
\mforall{}[z:formula()]. \mforall{}[v0:\{a:formula()| a \msubseteq{} z \mwedge{} (\muparrow{}pvar?(a))\} {}\mrightarrow{} \mBbbB{}]. \mforall{}[f:\{f:\{a:formula()| a \msubseteq{} z\} {}\mrightarrow{} \mBbbB{}|
valuation(v0;z;f)\} ].
f z = extend-val(v0;f;z)
Date html generated:
2016_05_15-PM-07_17_20
Last ObjectModification:
2015_12_27-AM-11_29_12
Theory : general
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