Nuprl Lemma : sq_or_functionality_wrt_iff
∀[P1,P2,Q1,Q2:ℙ]. ({P1 ⇐⇒ P2} ⇒ {Q1 ⇐⇒ Q2} ⇒ {P1 ↓∨ Q1 ⇐⇒ P2 ↓∨ Q2})
Proof
Definitions occuring in Statement :
sq_or: a ↓∨ b,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
iff: P ⇐⇒ Q,
implies: P ⇒ Q
Definitions unfolded in proof :
guard: {T},
sq_or: a ↓∨ b,
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
squash: ↓T,
or: P ∨ Q,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
iff_wf,
or_wf,
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
imageElimination,
unionElimination,
independent_functionElimination,
hypothesis,
inlFormation,
hypothesisEquality,
imageMemberEquality,
baseClosed,
inrFormation,
lemma_by_obid,
isectElimination,
lambdaEquality,
dependent_functionElimination,
independent_pairEquality,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[P1,P2,Q1,Q2:\mBbbP{}]. (\{P1 \mLeftarrow{}{}\mRightarrow{} P2\} {}\mRightarrow{} \{Q1 \mLeftarrow{}{}\mRightarrow{} Q2\} {}\mRightarrow{} \{P1 \mdownarrow{}\mvee{} Q1 \mLeftarrow{}{}\mRightarrow{} P2 \mdownarrow{}\mvee{} Q2\})
Date html generated:
2016_05_13-PM-03_13_28
Last ObjectModification:
2016_01_06-PM-05_48_08
Theory : core_2
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