Nuprl Lemma : and_functionality_wrt_uimplies
∀[P1,P2,Q1,Q2:ℙ]. ({P2 supposing P1} ⇒ {Q2 supposing Q1} ⇒ {P2 ∧ Q2 supposing P1 ∧ Q1})
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
uimplies: b supposing a,
and: P ∧ Q,
cand: A c∧ B,
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,
cut,
hypothesis,
sqequalHypSubstitution,
independent_isectElimination,
thin,
productElimination,
independent_pairFormation,
Error :productIsType,
Error :universeIsType,
hypothesisEquality,
introduction,
extract_by_obid,
isectElimination,
cumulativity,
lambdaEquality,
Error :inhabitedIsType,
universeEquality
Latex:
\mforall{}[P1,P2,Q1,Q2:\mBbbP{}]. (\{P2 supposing P1\} {}\mRightarrow{} \{Q2 supposing Q1\} {}\mRightarrow{} \{P2 \mwedge{} Q2 supposing P1 \mwedge{} Q1\})
Date html generated:
2019_06_20-AM-11_14_12
Last ObjectModification:
2018_09_26-AM-10_41_48
Theory : core_2
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