Nuprl Lemma : uiff_functionality_wrt_uiff2
∀[P1,P2,Q1,Q2:ℙ]. ({P1 ⇐⇒ P2} ⇒ {Q1 ⇐⇒ Q2} ⇒ {uiff(P1;Q1) ⇐⇒ uiff(P2;Q2)})
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
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,
uiff: uiff(P;Q),
uimplies: b supposing a,
prop: ℙ,
member: t ∈ T,
rev_implies: P ⇐ Q
Lemmas referenced :
uiff_wf,
and_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
cut,
hypothesis,
independent_functionElimination,
independent_isectElimination,
Error :universeIsType,
hypothesisEquality,
introduction,
extract_by_obid,
isectElimination,
functionEquality,
cumulativity,
Error :inhabitedIsType,
universeEquality
Latex:
\mforall{}[P1,P2,Q1,Q2:\mBbbP{}]. (\{P1 \mLeftarrow{}{}\mRightarrow{} P2\} {}\mRightarrow{} \{Q1 \mLeftarrow{}{}\mRightarrow{} Q2\} {}\mRightarrow{} \{uiff(P1;Q1) \mLeftarrow{}{}\mRightarrow{} uiff(P2;Q2)\})
Date html generated:
2019_06_20-AM-11_14_08
Last ObjectModification:
2018_09_26-AM-10_41_46
Theory : core_2
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