Nuprl Lemma : binrel_eqv_transitivity
∀[T:Type]. ∀[Q,R,S:T ⟶ T ⟶ ℙ]. ((Q <≡>{T} R) ⇒ (R <≡>{T} S) ⇒ (Q <≡>{T} S))
Proof
Definitions occuring in Statement :
binrel_eqv: E <≡>{T} E',
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
binrel_eqv: E <≡>{T} E',
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
all_wf,
iff_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
cut,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
productElimination,
independent_functionElimination,
because_Cache,
applyEquality,
lemma_by_obid,
isectElimination,
lambdaEquality,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[Q,R,S:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. ((Q <\mequiv{}>\{T\} R) {}\mRightarrow{} (R <\mequiv{}>\{T\} S) {}\mRightarrow{} (Q <\mequiv{}>\{T\} S))
Date html generated:
2016_05_14-PM-03_54_40
Last ObjectModification:
2015_12_26-PM-06_56_07
Theory : relations2
Home
Index