Nuprl Lemma : fo-logic-test1
∀x.(B x) ⇒ (C x) ⇒ ∃x.B x ⇒ ∃x.C x
Proof
Definitions occuring in Statement :
language1: language1{i:l}(D,A,B,C,P,Q,R,H.fml[D;A;B;C;P;Q;R;H]),
forsome: ∃x.P[x],
forall: ∀x.P[x],
implies: P ⇒ Q,
apply: f a
Definitions unfolded in proof :
language1: language1{i:l}(D,A,B,C,P,Q,R,H.fml[D;A;B;C;P;Q;R;H]),
uall: ∀[x:A]. B[x],
!hyp_hide: x,
member: t ∈ T,
prop: ℙ,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
forsome: ∃x.P[x],
exists: ∃x:A. B[x],
forall: ∀x.P[x],
all: ∀x:A. B[x]
Lemmas referenced :
forsome_wf,
forall_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalHypSubstitution,
functionEquality,
cumulativity,
hypothesisEquality,
universeEquality,
because_Cache,
lambdaFormation,
cut,
lemma_by_obid,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesis,
productElimination,
addLevel,
dependent_functionElimination,
levelHypothesis,
independent_functionElimination,
dependent_pairFormation
Latex:
\mforall{}x.(B x) {}\mRightarrow{} (C x) {}\mRightarrow{} \mexists{}x.B x {}\mRightarrow{} \mexists{}x.C x
Date html generated:
2016_05_16-AM-09_07_56
Last ObjectModification:
2015_12_28-PM-07_03_18
Theory : first-order!and!ancestral!logic
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