Nuprl Lemma : uimplies_transitivity
∀[P,Q,R:ℙ]. (Q supposing P ⇒ R supposing Q ⇒ {R supposing P})
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
implies: P ⇒ Q
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
uimplies: b supposing a,
prop: ℙ,
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
isect_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
lambdaFormation,
sqequalHypSubstitution,
independent_isectElimination,
thin,
hypothesis,
Error :universeIsType,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
isectElimination,
cumulativity,
lambdaEquality,
Error :inhabitedIsType,
universeEquality
Latex:
\mforall{}[P,Q,R:\mBbbP{}]. (Q supposing P {}\mRightarrow{} R supposing Q {}\mRightarrow{} \{R supposing P\})
Date html generated:
2019_06_20-AM-11_14_21
Last ObjectModification:
2018_09_26-AM-10_41_52
Theory : core_2
Home
Index