Nuprl Lemma : sq_stable_and_left_false
∀[P:ℙ]. ∀Q:Top. ((¬P) ⇒ SqStable(P ∧ Q))
Proof
Definitions occuring in Statement :
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
top: Top,
prop: ℙ,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
sq_stable: SqStable(P),
squash: ↓T,
false: False,
and: P ∧ Q,
not: ¬A,
member: t ∈ T,
prop: ℙ
Lemmas referenced :
squash_wf,
not_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
sqequalHypSubstitution,
imageElimination,
productElimination,
thin,
independent_functionElimination,
hypothesis,
voidElimination,
lemma_by_obid,
isectElimination,
productEquality,
cumulativity,
hypothesisEquality,
universeEquality
Latex:
\mforall{}[P:\mBbbP{}]. \mforall{}Q:Top. ((\mneg{}P) {}\mRightarrow{} SqStable(P \mwedge{} Q))
Date html generated:
2016_05_15-PM-03_14_23
Last ObjectModification:
2015_12_27-PM-01_02_10
Theory : general
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