Nuprl Lemma : dl-prop-deq_wf
dl-prop-deq() ∈ EqDecider(Prop)
Proof
Definitions occuring in Statement :
dl-prop-deq: dl-prop-deq(),
dl-prop: Prop,
deq: EqDecider(T),
member: t ∈ T
Definitions unfolded in proof :
dl-prop-deq: dl-prop-deq(),
member: t ∈ T,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
dl-obj-prop: dl-obj-prop(x),
pi2: snd(t),
dl-prop-obj: prop(x),
uimplies: b supposing a,
prop: ℙ,
dl-kind: dl-kind(d),
mobj-kind: mobj-kind(x),
pi1: fst(t),
subtype_rel: A ⊆r B
Lemmas referenced :
dlo_eq_wf,
dl-prop-obj_wf,
dl-prop_wf,
istype-assert,
assert-dlo_eq,
dl-obj-prop_wf,
equal_wf,
dl-Obj_wf,
dl-kind_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_set_memberEquality_alt,
lambdaEquality_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
inhabitedIsType,
universeIsType,
lambdaFormation_alt,
independent_pairFormation,
sqequalRule,
equalityIstype,
applyEquality,
functionIsType,
because_Cache,
productIsType,
productElimination,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
setElimination,
rename,
independent_isectElimination,
hyp_replacement,
tokenEquality,
atomEquality
Latex:
dl-prop-deq() \mmember{} EqDecider(Prop)
Date html generated:
2019_10_15-AM-11_43_07
Last ObjectModification:
2019_05_11-AM-11_25_58
Theory : dynamic!logic
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