Nuprl Lemma : EquatePairs_wf
∀[x,y,n,m:Base].
(EquatePairs(x;n;y;m) ∈ Type) supposing ((¬(n = m ∈ Base)) and (¬(x = m ∈ Base)) and (¬(y = n ∈ Base)))
Proof
Definitions occuring in Statement :
EquatePairs: EquatePairs(x;n;y;m),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
member: t ∈ T,
base: Base,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
EquatePairs: EquatePairs(x;n;y;m),
so_lambda: λ2x y.t[x; y],
prop: ℙ,
or: P ∨ Q,
and: P ∧ Q,
so_apply: x[s1;s2],
not: ¬A,
implies: P ⇒ Q,
false: False,
all: ∀x:A. B[x],
cand: A c∧ B,
guard: {T}
Lemmas referenced :
pertype_wf,
equal-wf-base,
base_wf,
istype-void,
istype-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
Error :lambdaEquality_alt,
unionEquality,
hypothesis,
hypothesisEquality,
productEquality,
because_Cache,
Error :inhabitedIsType,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :functionIsType,
Error :equalityIstype,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
Error :lambdaFormation_alt,
unionElimination,
Error :inlFormation_alt,
Error :unionIsType,
Error :productIsType,
productElimination,
Error :inrFormation_alt,
independent_pairFormation,
independent_functionElimination,
voidElimination
Latex:
\mforall{}[x,y,n,m:Base]. (EquatePairs(x;n;y;m) \mmember{} Type) supposing ((\mneg{}(n = m)) and (\mneg{}(x = m)) and (\mneg{}(y = n)))
Date html generated:
2019_06_20-PM-02_44_14
Last ObjectModification:
2019_01_13-PM-03_28_12
Theory : num_thy_1
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