Nuprl Lemma : coW-equiv_transitivity
∀[A:𝕌']. ∀[B:A ⟶ Type]. ∀[w1,w2,w3:coW(A;a.B[a])].
(coW-equiv(a.B[a];w1;w2) ⇒ coW-equiv(a.B[a];w2;w3) ⇒ coW-equiv(a.B[a];w1;w3))
Proof
Definitions occuring in Statement :
coW-equiv: coW-equiv(a.B[a];w;w'),
coW: coW(A;a.B[a]),
uall: ∀[x:A]. B[x],
so_apply: x[s],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
prop: ℙ,
so_apply: x[s],
so_lambda: λ2x.t[x],
member: t ∈ T,
win2: win2(g),
coW-equiv: coW-equiv(a.B[a];w;w'),
implies: P ⇒ Q,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coW_wf,
coW-equiv_wf,
nat_wf,
coW-trans_wf
Rules used in proof :
universeEquality,
functionEquality,
cumulativity,
instantiate,
applyEquality,
lambdaEquality,
sqequalRule,
extract_by_obid,
introduction,
rename,
hypothesisEquality,
thin,
isectElimination,
hypothesis,
cut,
sqequalHypSubstitution,
lambdaFormation,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A:\mBbbU{}']. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[w1,w2,w3:coW(A;a.B[a])].
(coW-equiv(a.B[a];w1;w2) {}\mRightarrow{} coW-equiv(a.B[a];w2;w3) {}\mRightarrow{} coW-equiv(a.B[a];w1;w3))
Date html generated:
2018_07_25-PM-01_47_56
Last ObjectModification:
2018_07_11-PM-00_11_45
Theory : co-recursion
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