Nuprl Lemma : eq-in-quot
∀A:Type. ∀a,b:⇃(A). (a = b ∈ ⇃(A))
Proof
Definitions occuring in Statement :
quotient: x,y:A//B[x; y],
all: ∀x:A. B[x],
true: True,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
quotient: x,y:A//B[x; y],
and: P ∧ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
quotient_wf,
equal-wf-base,
equiv_rel_true,
true_wf,
quotient-member-eq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
pointwiseFunctionalityForEquality,
because_Cache,
sqequalHypSubstitution,
sqequalRule,
pertypeElimination,
productElimination,
thin,
hypothesis,
lemma_by_obid,
isectElimination,
lambdaEquality,
cumulativity,
hypothesisEquality,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
productEquality,
universeEquality
Latex:
\mforall{}A:Type. \mforall{}a,b:\00D9(A). (a = b)
Date html generated:
2016_05_14-AM-06_08_47
Last ObjectModification:
2016_05_13-PM-00_09_22
Theory : quot_1
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