Nuprl Lemma : implies_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},
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
rev_implies_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
lambdaFormation,
hypothesisEquality,
functionEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
Error :inhabitedIsType,
Error :universeIsType,
universeEquality,
independent_functionElimination
Latex:
\mforall{}[P1,P2,Q1,Q2:\mBbbP{}]. (\{P1 \mLeftarrow{}{} P2\} {}\mRightarrow{} \{Q1 {}\mRightarrow{} Q2\} {}\mRightarrow{} \{(P1 {}\mRightarrow{} Q1) {}\mRightarrow{} P2 {}\mRightarrow{} Q2\})
Date html generated:
2019_06_20-AM-11_16_54
Last ObjectModification:
2018_09_26-AM-10_24_29
Theory : core_2
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