Nuprl Lemma : sp_refl_cl_le_rel
∀[T:Type]. ∀[r:T ⟶ T ⟶ ℙ]. ((ro\) ≡>{T} r)
Proof
Definitions occuring in Statement :
s_part: E\,
refl_cl: Eo,
binrel_le: E ≡>{T} E',
uall: ∀[x:A]. B[x],
prop: ℙ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
refl_cl: Eo,
s_part: E\,
binrel_le: E ≡>{T} E',
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
member: t ∈ T,
prop: ℙ,
or: P ∨ Q,
not: ¬A,
false: False
Lemmas referenced :
and_wf,
or_wf,
equal_wf,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
applyEquality,
functionEquality,
cumulativity,
universeEquality,
unionElimination,
equalitySymmetry,
independent_functionElimination,
inlFormation,
voidElimination
Latex:
\mforall{}[T:Type]. \mforall{}[r:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. ((r\msupzero{}\mbackslash{}) \mequiv{}>\{T\} r)
Date html generated:
2016_05_15-PM-00_02_08
Last ObjectModification:
2015_12_26-PM-11_25_40
Theory : gen_algebra_1
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