Nuprl Lemma : exists_uni_upto_wf
∀T:Type. ∀r:T ⟶ T ⟶ ℙ. ∀Q:T ⟶ ℙ. ((r)∃!x:T. Q[x] ∈ ℙ)
Proof
Definitions occuring in Statement :
exists_uni_upto: exists_uni_upto,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
exists_uni_upto: exists_uni_upto,
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
exists_wf,
uni_sat_upto_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
dependent_functionElimination,
applyEquality,
hypothesis,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}T:Type. \mforall{}r:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}. \mforall{}Q:T {}\mrightarrow{} \mBbbP{}. ((r)\mexists{}!x:T. Q[x] \mmember{} \mBbbP{})
Date html generated:
2016_05_16-AM-07_45_13
Last ObjectModification:
2015_12_28-PM-05_53_41
Theory : factor_1
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