Nuprl Lemma : strict-fun-connected_irreflexivity
∀[T:Type]. ∀[f:T ⟶ T]. ∀[x:T]. False supposing x = f+(x)
Proof
Definitions occuring in Statement :
strict-fun-connected: y = f+(x),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
false: False,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
strict-fun-connected: y = f+(x),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
false: False,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
and_wf,
not_wf,
equal_wf,
fun-connected_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
independent_functionElimination,
hypothesisEquality,
voidElimination,
because_Cache,
lemma_by_obid,
isectElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[f:T {}\mrightarrow{} T]. \mforall{}[x:T]. False supposing x = f+(x)
Date html generated:
2016_05_15-PM-04_59_21
Last ObjectModification:
2015_12_27-PM-02_29_33
Theory : general
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