Nuprl Lemma : xxirrefl_wf
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. (irrefl(T;R) ∈ ℙ)
Proof
Definitions occuring in Statement :
xxirrefl: irrefl(T;R),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
xxirrefl: irrefl(T;R),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
prop: ℙ
Lemmas referenced :
irrefl_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (irrefl(T;R) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-00_01_01
Last ObjectModification:
2015_12_26-PM-11_26_32
Theory : gen_algebra_1
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