Nuprl Lemma : binrel_eqv_inversion
∀[T:Type]. ∀[r,r':T ⟶ T ⟶ ℙ]. ((r <≡>{T} r') ⇒ (r' <≡>{T} r))
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],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
all_wf,
iff_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
hypothesisEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
lambdaEquality,
applyEquality,
hypothesis,
functionEquality,
cumulativity,
universeEquality,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
addLevel,
productElimination,
independent_pairFormation,
impliesFunctionality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[r,r':T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. ((r <\mequiv{}>\{T\} r') {}\mRightarrow{} (r' <\mequiv{}>\{T\} r))
Date html generated:
2016_05_14-PM-03_54_44
Last ObjectModification:
2015_12_26-PM-06_56_05
Theory : relations2
Home
Index