Nuprl Lemma : eq_atom_eq_true_elim_sqequal
∀[x,y:Atom]. x = y ∈ Atom supposing x =a y ~ tt
Proof
Definitions occuring in Statement :
eq_atom: x =a y,
btrue: tt,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
atom: Atom,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
assert_of_eq_atom,
atom_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
sqequalIntensionalEquality,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
applyEquality,
thin,
lemma_by_obid,
sqequalHypSubstitution,
because_Cache,
isect_memberEquality,
isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
atomEquality,
natural_numberEquality,
productElimination,
independent_isectElimination
Latex:
\mforall{}[x,y:Atom]. x = y supposing x =a y \msim{} tt
Date html generated:
2016_05_13-PM-04_10_30
Last ObjectModification:
2016_01_18-PM-05_39_33
Theory : subtype_1
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