Nuprl Lemma : implies_functionality_wrt_iff
∀[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},
iff: P ⇐⇒ Q,
implies: P ⇒ Q
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
iff_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
hypothesisEquality,
functionEquality,
independent_functionElimination,
hypothesis,
cut,
introduction,
extract_by_obid,
isectElimination,
Error :inhabitedIsType,
Error :universeIsType,
universeEquality
Latex:
\mforall{}[P1,P2,Q1,Q2:\mBbbP{}]. (\{P1 \mLeftarrow{}{}\mRightarrow{} P2\} {}\mRightarrow{} \{Q1 \mLeftarrow{}{}\mRightarrow{} Q2\} {}\mRightarrow{} \{P1 {}\mRightarrow{} Q1 \mLeftarrow{}{}\mRightarrow{} P2 {}\mRightarrow{} Q2\})
Date html generated:
2019_06_20-AM-11_16_51
Last ObjectModification:
2018_09_26-AM-10_24_28
Theory : core_2
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