Nuprl Lemma : cand_functionality_wrt_iff
∀[a1,a2,b1,b2:ℙ]. ((a1 ⇐⇒ a2) ⇒ (b1 ⇐⇒ b2) ⇒ (a1 c∧ b1 ⇐⇒ a2 c∧ b2))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
cand: A c∧ B,
prop: ℙ,
iff: P ⇐⇒ Q,
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
cand: A c∧ B,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
iff_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
productEquality,
cumulativity,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
isectElimination,
hypothesis,
inhabitedIsType,
universeIsType,
universeEquality,
independent_functionElimination
Latex:
\mforall{}[a1,a2,b1,b2:\mBbbP{}]. ((a1 \mLeftarrow{}{}\mRightarrow{} a2) {}\mRightarrow{} (b1 \mLeftarrow{}{}\mRightarrow{} b2) {}\mRightarrow{} (a1 c\mwedge{} b1 \mLeftarrow{}{}\mRightarrow{} a2 c\mwedge{} b2))
Date html generated:
2019_10_15-AM-10_46_37
Last ObjectModification:
2018_09_27-AM-09_41_12
Theory : basic
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