Nuprl Lemma : approx-per-for-mono
∀[T:Type]. ∀x,y:Base. approx-per(T;x;y) supposing x = y ∈ T supposing mono(T)
Proof
Definitions occuring in Statement :
approx-per: approx-per(T;x;y),
mono: mono(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
base: Base,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
exists: ∃x:A. B[x],
cand: A c∧ B,
and: P ∧ Q,
approx-per: approx-per(T;x;y),
prop: ℙ,
implies: P ⇒ Q,
all: ∀x:A. B[x],
mono: mono(T),
member: t ∈ T,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
is-above: is-above(T;a;z)
Lemmas referenced :
mono_wf,
equal-wf-base-T,
is-exception_wf,
has-value_wf_base,
equal-wf-base,
sqle_wf_base,
base_wf,
is-above_wf
Rules used in proof :
universeEquality,
productElimination,
productEquality,
equalitySymmetry,
equalityTransitivity,
sqleReflexivity,
divergentSqle,
because_Cache,
dependent_pairFormation,
independent_pairFormation,
lambdaFormation,
rename,
cumulativity,
isectElimination,
extract_by_obid,
hypothesis,
axiomEquality,
hypothesisEquality,
thin,
dependent_functionElimination,
lambdaEquality,
sqequalHypSubstitution,
sqequalRule,
introduction,
cut,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}x,y:Base. approx-per(T;x;y) supposing x = y supposing mono(T)
Date html generated:
2018_05_21-PM-00_04_28
Last ObjectModification:
2017_12_30-PM-02_03_09
Theory : rel_1
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