Nuprl Lemma : strict_part_irrefl
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[a,b:T]. ¬(a = b ∈ T) supposing strict_part(x,y.R[x;y];a;b)
Proof
Definitions occuring in Statement :
strict_part: strict_part(x,y.R[x; y];a;b),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
not: ¬A,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
not: ¬A,
strict_part: strict_part(x,y.R[x; y];a;b),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
implies: P ⇒ Q,
false: False,
and: P ∧ Q,
prop: ℙ,
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
guard: {T}
Lemmas referenced :
equal_wf,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
lambdaEquality,
dependent_functionElimination,
because_Cache,
productEquality,
applyEquality,
functionExtensionality,
universeEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
voidElimination,
hyp_replacement,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}[a,b:T]. \mneg{}(a = b) supposing strict\_part(x,y.R[x;y];a;b)
Date html generated:
2017_04_14-AM-07_37_51
Last ObjectModification:
2017_02_27-PM-03_09_48
Theory : rel_1
Home
Index