Nuprl Lemma : sq-decider-atom-deq
sq-decider(AtomDeq)
Proof
Definitions occuring in Statement :
atom-deq: AtomDeq,
sq-decider: sq-decider(eq)
Definitions unfolded in proof :
atom-deq: AtomDeq,
sq-decider: sq-decider(eq),
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
uimplies: b supposing a,
exists: ∃x:A. B[x],
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
has-value: (a)↓,
eq_atom: x =a y,
and: P ∧ Q,
uiff: uiff(P;Q),
subtype_rel: A ⊆r B,
assert: ↑b,
ifthenelse: if b then t else f fi ,
true: True
Lemmas referenced :
atom_subtype_base,
assert_of_eq_atom,
is-exception_wf,
has-value_wf_base,
base_wf,
exists_wf,
subtype_rel_self,
subtype_base_sq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
independent_isectElimination,
hypothesis,
productElimination,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
lambdaEquality,
sqequalIntensionalEquality,
baseApply,
closedConclusion,
baseClosed,
sqequalAxiom,
isect_memberEquality,
divergentSqle,
sqleReflexivity,
callbyvalueAtomEq,
equalityTransitivity,
equalitySymmetry,
applyEquality,
natural_numberEquality
Latex:
sq-decider(AtomDeq)
Date html generated:
2016_05_14-AM-06_07_08
Last ObjectModification:
2016_01_14-PM-07_31_52
Theory : equality!deciders
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