Nuprl Lemma : fo-logic-xmiddle
∀x:Dom. ((((B x) ∨ ((B x) ⇒ A)) ⇒ A) ⇒ A)
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]),
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: 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,
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
or: P ∨ Q
Lemmas referenced :
or_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,
applyEquality,
hypothesis,
addLevel,
independent_functionElimination,
levelHypothesis,
sqequalRule,
inrFormation,
inlFormation
Latex:
\mforall{}x:Dom. ((((B x) \mvee{} ((B x) {}\mRightarrow{} A)) {}\mRightarrow{} A) {}\mRightarrow{} A)
Date html generated:
2016_05_16-AM-09_08_03
Last ObjectModification:
2015_12_28-PM-07_03_16
Theory : first-order!and!ancestral!logic
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