Nuprl Lemma : refl_cl_sp_le_rel
∀[T:Type]. ∀[r:T ⟶ T ⟶ ℙ]. (refl(T;r) ⇒ ((r\\00B8) ≡>{T} r))
Proof
Definitions occuring in Statement :
s_part: E\,
refl_cl: Eo,
xxrefl: refl(T;E),
binrel_le: E ≡>{T} E',
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
s_part: E\,
refl_cl: Eo,
binrel_le: E ≡>{T} E',
xxrefl: refl(T;E),
refl: Refl(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
or: P ∨ Q,
guard: {T}
Lemmas referenced :
or_wf,
equal_wf,
not_wf,
all_wf,
and_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
productEquality,
applyEquality,
functionExtensionality,
lambdaEquality,
universeEquality,
functionEquality,
unionElimination,
productElimination,
dependent_functionElimination,
hyp_replacement,
equalitySymmetry,
dependent_set_memberEquality,
independent_pairFormation,
setElimination,
rename,
setEquality
Latex:
\mforall{}[T:Type]. \mforall{}[r:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (refl(T;r) {}\mRightarrow{} ((r\mbackslash{}\msupzero{}) \mequiv{}>\{T\} r))
Date html generated:
2016_10_21-AM-11_25_09
Last ObjectModification:
2016_07_12-PM-01_05_42
Theory : gen_algebra_1
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