Nuprl Lemma : uiff_transitivity3
∀[P,Q,R:ℙ]. ((P = Q ∈ ℙ) ⇒ uiff(Q;R) ⇒ uiff(P;R))
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
prop: ℙ,
member: t ∈ T,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
uiff: uiff(P;Q)
Lemmas referenced :
iff_weakening_equal,
uiff_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
sqequalHypSubstitution,
hypothesis,
introduction,
extract_by_obid,
isectElimination,
thin,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
productElimination,
independent_pairFormation,
independent_functionElimination,
hypothesisEquality,
hyp_replacement,
Error :applyLambdaEquality,
sqequalRule,
instantiate,
universeEquality,
because_Cache
Latex:
\mforall{}[P,Q,R:\mBbbP{}]. ((P = Q) {}\mRightarrow{} uiff(Q;R) {}\mRightarrow{} uiff(P;R))
Date html generated:
2016_10_21-AM-09_34_50
Last ObjectModification:
2016_07_12-AM-04_59_35
Theory : core_2
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