Nuprl Lemma : sub-equality
∀[T:Type]. ∀[P:T ⟶ ℙ]. ∀[i,u:T]. (i = u ∈ {j:T| {j:T| P j} } ) supposing ((P u) and (i = u ∈ T))
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
applyEquality,
hypothesisEquality,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
functionEquality,
cumulativity,
universeEquality,
dependent_set_memberEquality,
setEquality,
lambdaEquality
Latex:
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. \mforall{}[i,u:T]. (i = u) supposing ((P u) and (i = u))
Date html generated:
2016_05_15-PM-03_38_03
Last ObjectModification:
2015_12_27-PM-01_16_12
Theory : general
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