Nuprl Lemma : simplify-equal-imp
∀[T:Type]. ∀[x,y,z:T]. uiff(x = z ∈ T supposing x = y ∈ T;¬(x = y ∈ T)) supposing ¬(y = z ∈ T)
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
equal_wf,
isect_wf,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
thin,
sqequalHypSubstitution,
independent_isectElimination,
hypothesis,
independent_functionElimination,
equalitySymmetry,
equalityTransitivity,
voidElimination,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
because_Cache,
isect_memberEquality,
axiomEquality,
productElimination,
independent_pairEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x,y,z:T]. uiff(x = z supposing x = y;\mneg{}(x = y)) supposing \mneg{}(y = z)
Date html generated:
2018_05_21-PM-06_32_49
Last ObjectModification:
2017_07_26-PM-04_51_50
Theory : general
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