Nuprl Lemma : b_all-inst
∀[B:Type]. ∀b:bag(B). ∀P:B ⟶ ℙ. ∀x:B. (x ↓∈ b ⇒ b_all(B;b;x.P[x]) ⇒ P[x])
Proof
Definitions occuring in Statement :
b_all: b_all(T;b;x.P[x]),
bag-member: x ↓∈ bs,
bag: bag(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
b_all: b_all(T;b;x.P[x])
Lemmas referenced :
b_all_wf,
bag-member_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesis,
functionEquality,
cumulativity,
universeEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[B:Type]. \mforall{}b:bag(B). \mforall{}P:B {}\mrightarrow{} \mBbbP{}. \mforall{}x:B. (x \mdownarrow{}\mmember{} b {}\mRightarrow{} b\_all(B;b;x.P[x]) {}\mRightarrow{} P[x])
Date html generated:
2016_05_15-PM-02_41_26
Last ObjectModification:
2015_12_27-AM-09_40_46
Theory : bags
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