Nuprl Lemma : bar-diverges_functionality
∀[T:Type]. ∀[x,y:bar-base(T)]. (bar-equal(T;x;y) ⇒ {x↑ ⇐⇒ y↑})
Proof
Definitions occuring in Statement :
bar-equal: bar-equal(T;x;y),
bar-diverges: x↑,
bar-base: bar-base(T),
uall: ∀[x:A]. B[x],
guard: {T},
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
not: ¬A,
false: False,
prop: ℙ,
bar-diverges: x↑,
all: ∀x:A. B[x],
bar-equal: bar-equal(T;x;y)
Lemmas referenced :
bar-diverges-iff,
bar-converges_wf,
bar-diverges_wf,
bar-equal_wf,
assert_wf,
isl_wf,
unit_wf2,
bar-val_wf,
nat_wf,
bar-base_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
independent_pairFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_functionElimination,
voidElimination,
because_Cache,
lambdaEquality,
dependent_functionElimination,
independent_pairEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x,y:bar-base(T)]. (bar-equal(T;x;y) {}\mRightarrow{} \{x\muparrow{} \mLeftarrow{}{}\mRightarrow{} y\muparrow{}\})
Date html generated:
2016_05_14-AM-06_20_37
Last ObjectModification:
2015_12_26-PM-00_00_35
Theory : co-recursion
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