Nuprl Lemma : and_functionality_wrt_implies
∀[P1,P2,Q1,Q2:ℙ]. ({P1 ⇒ P2} ⇒ {Q1 ⇒ Q2} ⇒ {(P1 ∧ Q1) ⇒ (P2 ∧ Q2)})
Proof
Definitions occuring in Statement :
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,
and: P ∧ Q,
cand: A c∧ B,
member: t ∈ T,
prop: ℙ
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
independent_functionElimination,
hypothesis,
independent_pairFormation,
productEquality,
cumulativity,
hypothesisEquality,
functionEquality,
Error :inhabitedIsType,
Error :universeIsType,
universeEquality
Latex:
\mforall{}[P1,P2,Q1,Q2:\mBbbP{}]. (\{P1 {}\mRightarrow{} P2\} {}\mRightarrow{} \{Q1 {}\mRightarrow{} Q2\} {}\mRightarrow{} \{(P1 \mwedge{} Q1) {}\mRightarrow{} (P2 \mwedge{} Q2)\})
Date html generated:
2019_06_20-AM-11_16_49
Last ObjectModification:
2018_09_26-AM-10_24_26
Theory : core_2
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