Nuprl Lemma : half-squash-equality
∀[Q:Type]. ∀[a,b:⇃(Q)]. (a = b ∈ ⇃(Q))
Proof
Definitions occuring in Statement :
quotient: x,y:A//B[x; y],
uall: ∀[x:A]. B[x],
true: True,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
true: True,
prop: ℙ
Lemmas referenced :
quotient-member-eq,
true_wf,
equiv_rel_true,
quotient_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
pointwiseFunctionalityForEquality,
because_Cache,
sqequalHypSubstitution,
sqequalRule,
pertypeElimination,
productElimination,
thin,
equalityTransitivity,
hypothesis,
equalitySymmetry,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
rename,
extract_by_obid,
isectElimination,
hypothesisEquality,
Error :lambdaEquality_alt,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
natural_numberEquality,
Error :equalityIsType1,
Error :universeIsType,
Error :productIsType,
Error :equalityIsType4,
Error :isect_memberEquality_alt,
axiomEquality,
Error :isectIsTypeImplies,
instantiate,
universeEquality
Latex:
\mforall{}[Q:Type]. \mforall{}[a,b:\00D9(Q)]. (a = b)
Date html generated:
2019_06_20-PM-00_32_44
Last ObjectModification:
2018_11_16-AM-11_46_10
Theory : quot_1
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