Nuprl Lemma : half-squash-stable__and
∀[P,Q:ℙ]. (half-squash-stable(P) ⇒ half-squash-stable(Q) ⇒ half-squash-stable(P ∧ Q))
Proof
Definitions occuring in Statement :
half-squash-stable: half-squash-stable(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
guard: {T},
uimplies: b supposing a,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
prop: ℙ,
member: t ∈ T,
cand: A c∧ B,
and: P ∧ Q,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
half-squash-stable: half-squash-stable(P)
Lemmas referenced :
implies-quotient-true,
equiv_rel_true,
true_wf,
quotient_wf
Rules used in proof :
promote_hyp,
independent_functionElimination,
productElimination,
universeEquality,
functionEquality,
independent_isectElimination,
because_Cache,
lambdaEquality,
hypothesisEquality,
cumulativity,
productEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
hypothesis,
independent_pairFormation,
cut,
lambdaFormation,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[P,Q:\mBbbP{}]. (half-squash-stable(P) {}\mRightarrow{} half-squash-stable(Q) {}\mRightarrow{} half-squash-stable(P \mwedge{} Q))
Date html generated:
2017_09_29-PM-05_48_10
Last ObjectModification:
2017_08_30-AM-11_07_04
Theory : quot_1
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