Nuprl Lemma : binrel_ap_functionality_wrt_breqv
∀[T:Type]. ∀[r,r':T ⟶ T ⟶ ℙ]. ∀a,b:T. ((r <≡>{T} r') ⇒ (a [r] b ⇐⇒ a [r'] b))
Proof
Definitions occuring in Statement :
binrel_ap: a [r] b,
binrel_eqv: E <≡>{T} E',
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
binrel_ap: a [r] b,
binrel_eqv: E <≡>{T} E',
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
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,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
hypothesis,
functionEquality,
cumulativity,
universeEquality,
dependent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[r,r':T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}a,b:T. ((r <\mequiv{}>\{T\} r') {}\mRightarrow{} (a [r] b \mLeftarrow{}{}\mRightarrow{} a [r'] b))
Date html generated:
2016_05_15-PM-00_00_40
Last ObjectModification:
2015_12_26-PM-11_26_35
Theory : gen_algebra_1
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