Nuprl Lemma : binrel_eqv_weakening
∀[T:Type]. ∀[E,E':T ⟶ T ⟶ ℙ]. E <≡>{T} E' supposing E = E' ∈ (T ⟶ T ⟶ ℙ)
Proof
Definitions occuring in Statement :
binrel_eqv: E <≡>{T} E',
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
binrel_eqv: E <≡>{T} E',
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
all: ∀x:A. B[x],
prop: ℙ,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
iff_weakening_equal,
true_wf,
squash_wf,
iff_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
cut,
introduction,
axiomEquality,
hypothesis,
thin,
rename,
lambdaFormation,
hypothesisEquality,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
functionEquality,
cumulativity,
universeEquality,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
imageMemberEquality,
baseClosed,
because_Cache,
independent_isectElimination,
productElimination,
independent_functionElimination,
independent_pairFormation
Latex:
\mforall{}[T:Type]. \mforall{}[E,E':T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. E <\mequiv{}>\{T\} E' supposing E = E'
Date html generated:
2016_05_14-PM-03_54_41
Last ObjectModification:
2016_01_14-PM-11_10_35
Theory : relations2
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